Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 619.8 | ||
Character | \(\chi\) | \(=\) | 1110.619 |
Dual form | 1110.2.ba.a.529.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.03441 | + | 1.98242i | 0.462602 | + | 0.886566i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −3.17295 | + | 1.83190i | −1.19926 | + | 0.692394i | −0.960391 | − | 0.278657i | \(-0.910111\pi\) |
−0.238871 | + | 0.971051i | \(0.576777\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.23403 | − | 0.0953865i | −0.706463 | − | 0.0301639i | ||||
\(11\) | 4.74886 | 1.43184 | 0.715918 | − | 0.698184i | \(-0.246008\pi\) | ||||
0.715918 | + | 0.698184i | \(0.246008\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −1.59526 | − | 2.76307i | −0.442445 | − | 0.766337i | 0.555425 | − | 0.831566i | \(-0.312555\pi\) |
−0.997870 | + | 0.0652294i | \(0.979222\pi\) | |||||||
\(14\) | − | 3.66381i | − | 0.979193i | ||||||
\(15\) | −1.88704 | − | 1.19962i | −0.487231 | − | 0.309741i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.99127 | + | 5.18104i | −0.725490 | + | 1.25659i | 0.233282 | + | 0.972409i | \(0.425054\pi\) |
−0.958772 | + | 0.284177i | \(0.908280\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −4.87068 | + | 2.81209i | −1.11741 | + | 0.645137i | −0.940739 | − | 0.339133i | \(-0.889866\pi\) |
−0.176672 | + | 0.984270i | \(0.556533\pi\) | |||||||
\(20\) | 1.19962 | − | 1.88704i | 0.268244 | − | 0.421954i | ||||
\(21\) | 1.83190 | − | 3.17295i | 0.399754 | − | 0.692394i | ||||
\(22\) | −2.37443 | + | 4.11264i | −0.506230 | + | 0.876817i | ||||
\(23\) | −2.02051 | −0.421305 | −0.210652 | − | 0.977561i | \(-0.567559\pi\) | ||||
−0.210652 | + | 0.977561i | \(0.567559\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | −2.86000 | + | 4.10127i | −0.571999 | + | 0.820254i | ||||
\(26\) | 3.19052 | 0.625712 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.17295 | + | 1.83190i | 0.599631 | + | 0.346197i | ||||
\(29\) | 3.80747i | 0.707030i | 0.935429 | + | 0.353515i | \(0.115014\pi\) | ||||
−0.935429 | + | 0.353515i | \(0.884986\pi\) | |||||||
\(30\) | 1.98242 | − | 1.03441i | 0.361939 | − | 0.188856i | ||||
\(31\) | − | 6.38718i | − | 1.14717i | −0.819146 | − | 0.573585i | \(-0.805552\pi\) | ||
0.819146 | − | 0.573585i | \(-0.194448\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −4.11264 | + | 2.37443i | −0.715918 | + | 0.413335i | ||||
\(34\) | −2.99127 | − | 5.18104i | −0.512999 | − | 0.888540i | ||||
\(35\) | −6.91373 | − | 4.39519i | −1.16863 | − | 0.742922i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.81681 | + | 1.77896i | 0.956278 | + | 0.292458i | ||||
\(38\) | − | 5.62418i | − | 0.912362i | ||||||
\(39\) | 2.76307 | + | 1.59526i | 0.442445 | + | 0.255446i | ||||
\(40\) | 1.03441 | + | 1.98242i | 0.163554 | + | 0.313448i | ||||
\(41\) | 0.175565 | + | 0.304088i | 0.0274187 | + | 0.0474905i | 0.879409 | − | 0.476067i | \(-0.157938\pi\) |
−0.851990 | + | 0.523557i | \(0.824605\pi\) | |||||||
\(42\) | 1.83190 | + | 3.17295i | 0.282669 | + | 0.489597i | ||||
\(43\) | 3.71753 | 0.566918 | 0.283459 | − | 0.958984i | \(-0.408518\pi\) | ||||
0.283459 | + | 0.958984i | \(0.408518\pi\) | |||||||
\(44\) | −2.37443 | − | 4.11264i | −0.357959 | − | 0.620003i | ||||
\(45\) | 2.23403 | + | 0.0953865i | 0.333030 | + | 0.0142194i | ||||
\(46\) | 1.01025 | − | 1.74981i | 0.148954 | − | 0.257995i | ||||
\(47\) | − | 10.1274i | − | 1.47723i | −0.674130 | − | 0.738613i | \(-0.735481\pi\) | ||
0.674130 | − | 0.738613i | \(-0.264519\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 3.21173 | − | 5.56289i | 0.458819 | − | 0.794698i | ||||
\(50\) | −2.12181 | − | 4.52746i | −0.300069 | − | 0.640280i | ||||
\(51\) | − | 5.98255i | − | 0.837724i | ||||||
\(52\) | −1.59526 | + | 2.76307i | −0.221222 | + | 0.383168i | ||||
\(53\) | −6.59610 | − | 3.80826i | −0.906044 | − | 0.523105i | −0.0268878 | − | 0.999638i | \(-0.508560\pi\) |
−0.879156 | + | 0.476534i | \(0.841893\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 4.91227 | + | 9.41425i | 0.662370 | + | 1.26942i | ||||
\(56\) | −3.17295 | + | 1.83190i | −0.424003 | + | 0.244798i | ||||
\(57\) | 2.81209 | − | 4.87068i | 0.372470 | − | 0.645137i | ||||
\(58\) | −3.29737 | − | 1.90374i | −0.432966 | − | 0.249973i | ||||
\(59\) | −8.74371 | − | 5.04818i | −1.13833 | − | 0.657217i | −0.192316 | − | 0.981333i | \(-0.561600\pi\) |
−0.946018 | + | 0.324116i | \(0.894933\pi\) | |||||||
\(60\) | −0.0953865 | + | 2.23403i | −0.0123143 | + | 0.288412i | ||||
\(61\) | −13.3043 | + | 7.68125i | −1.70344 | + | 0.983483i | −0.761220 | + | 0.648493i | \(0.775399\pi\) |
−0.942222 | + | 0.334990i | \(0.891267\pi\) | |||||||
\(62\) | 5.53146 | + | 3.19359i | 0.702496 | + | 0.405586i | ||||
\(63\) | 3.66381i | 0.461596i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.82742 | − | 6.02062i | 0.474733 | − | 0.746766i | ||||
\(66\) | − | 4.74886i | − | 0.584545i | ||||||
\(67\) | −0.485927 | + | 0.280550i | −0.0593654 | + | 0.0342746i | −0.529389 | − | 0.848379i | \(-0.677579\pi\) |
0.470024 | + | 0.882654i | \(0.344245\pi\) | |||||||
\(68\) | 5.98255 | 0.725490 | ||||||||
\(69\) | 1.74981 | − | 1.01025i | 0.210652 | − | 0.121620i | ||||
\(70\) | 7.26321 | − | 3.78987i | 0.868119 | − | 0.452977i | ||||
\(71\) | −6.31722 | − | 10.9417i | −0.749716 | − | 1.29855i | −0.947959 | − | 0.318393i | \(-0.896857\pi\) |
0.198243 | − | 0.980153i | \(-0.436477\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | − | 2.67482i | − | 0.313064i | −0.987673 | − | 0.156532i | \(-0.949969\pi\) | ||
0.987673 | − | 0.156532i | \(-0.0500315\pi\) | |||||||
\(74\) | −4.44903 | + | 4.14803i | −0.517189 | + | 0.482199i | ||||
\(75\) | 0.426193 | − | 4.98180i | 0.0492126 | − | 0.575249i | ||||
\(76\) | 4.87068 | + | 2.81209i | 0.558705 | + | 0.322569i | ||||
\(77\) | −15.0679 | + | 8.69945i | −1.71715 | + | 0.991395i | ||||
\(78\) | −2.76307 | + | 1.59526i | −0.312856 | + | 0.180627i | ||||
\(79\) | 1.65563 | − | 0.955880i | 0.186273 | − | 0.107545i | −0.403964 | − | 0.914775i | \(-0.632368\pi\) |
0.590237 | + | 0.807230i | \(0.299034\pi\) | |||||||
\(80\) | −2.23403 | − | 0.0953865i | −0.249772 | − | 0.0106645i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.351130 | −0.0387759 | ||||||||
\(83\) | −4.66513 | − | 2.69342i | −0.512065 | − | 0.295641i | 0.221617 | − | 0.975134i | \(-0.428866\pi\) |
−0.733682 | + | 0.679493i | \(0.762200\pi\) | |||||||
\(84\) | −3.66381 | −0.399754 | ||||||||
\(85\) | −13.3652 | − | 0.570654i | −1.44966 | − | 0.0618961i | ||||
\(86\) | −1.85877 | + | 3.21948i | −0.200436 | + | 0.347165i | ||||
\(87\) | −1.90374 | − | 3.29737i | −0.204102 | − | 0.353515i | ||||
\(88\) | 4.74886 | 0.506230 | ||||||||
\(89\) | 10.8009 | + | 6.23589i | 1.14489 | + | 0.661003i | 0.947637 | − | 0.319349i | \(-0.103464\pi\) |
0.197254 | + | 0.980352i | \(0.436798\pi\) | |||||||
\(90\) | −1.19962 | + | 1.88704i | −0.126451 | + | 0.198911i | ||||
\(91\) | 10.1233 | + | 5.84471i | 1.06121 | + | 0.612692i | ||||
\(92\) | 1.01025 | + | 1.74981i | 0.105326 | + | 0.182430i | ||||
\(93\) | 3.19359 | + | 5.53146i | 0.331160 | + | 0.573585i | ||||
\(94\) | 8.77054 | + | 5.06368i | 0.904612 | + | 0.522278i | ||||
\(95\) | −10.6130 | − | 6.74689i | −1.08887 | − | 0.692217i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | −3.07545 | −0.312265 | −0.156133 | − | 0.987736i | \(-0.549903\pi\) | ||||
−0.156133 | + | 0.987736i | \(0.549903\pi\) | |||||||
\(98\) | 3.21173 | + | 5.56289i | 0.324434 | + | 0.561936i | ||||
\(99\) | 2.37443 | − | 4.11264i | 0.238639 | − | 0.413335i | ||||
\(100\) | 4.98180 | + | 0.426193i | 0.498180 | + | 0.0426193i | ||||
\(101\) | 3.88128 | 0.386202 | 0.193101 | − | 0.981179i | \(-0.438146\pi\) | ||||
0.193101 | + | 0.981179i | \(0.438146\pi\) | |||||||
\(102\) | 5.18104 | + | 2.99127i | 0.512999 | + | 0.296180i | ||||
\(103\) | −0.530142 | −0.0522364 | −0.0261182 | − | 0.999659i | \(-0.508315\pi\) | ||||
−0.0261182 | + | 0.999659i | \(0.508315\pi\) | |||||||
\(104\) | −1.59526 | − | 2.76307i | −0.156428 | − | 0.270941i | ||||
\(105\) | 8.18506 | + | 0.349478i | 0.798780 | + | 0.0341055i | ||||
\(106\) | 6.59610 | − | 3.80826i | 0.640670 | − | 0.369891i | ||||
\(107\) | −9.43365 | + | 5.44652i | −0.911986 | + | 0.526535i | −0.881069 | − | 0.472987i | \(-0.843176\pi\) |
−0.0309161 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 4.73143 | + | 2.73169i | 0.453188 | + | 0.261648i | 0.709176 | − | 0.705032i | \(-0.249067\pi\) |
−0.255987 | + | 0.966680i | \(0.582401\pi\) | |||||||
\(110\) | −10.6091 | − | 0.452978i | −1.01154 | − | 0.0431897i | ||||
\(111\) | −5.92699 | + | 1.36779i | −0.562565 | + | 0.129825i | ||||
\(112\) | − | 3.66381i | − | 0.346197i | ||||||
\(113\) | 5.15391 | − | 8.92683i | 0.484839 | − | 0.839766i | −0.515009 | − | 0.857185i | \(-0.672211\pi\) |
0.999848 | + | 0.0174187i | \(0.00554482\pi\) | |||||||
\(114\) | 2.81209 | + | 4.87068i | 0.263376 | + | 0.456181i | ||||
\(115\) | −2.09003 | − | 4.00550i | −0.194896 | − | 0.373514i | ||||
\(116\) | 3.29737 | − | 1.90374i | 0.306153 | − | 0.176758i | ||||
\(117\) | −3.19052 | −0.294963 | ||||||||
\(118\) | 8.74371 | − | 5.04818i | 0.804924 | − | 0.464723i | ||||
\(119\) | − | 21.9189i | − | 2.00930i | ||||||
\(120\) | −1.88704 | − | 1.19962i | −0.172262 | − | 0.109510i | ||||
\(121\) | 11.5517 | 1.05015 | ||||||||
\(122\) | − | 15.3625i | − | 1.39085i | ||||||
\(123\) | −0.304088 | − | 0.175565i | −0.0274187 | − | 0.0158302i | ||||
\(124\) | −5.53146 | + | 3.19359i | −0.496739 | + | 0.286793i | ||||
\(125\) | −11.0889 | − | 1.42733i | −0.991817 | − | 0.127664i | ||||
\(126\) | −3.17295 | − | 1.83190i | −0.282669 | − | 0.163199i | ||||
\(127\) | −11.4248 | − | 6.59611i | −1.01379 | − | 0.585310i | −0.101488 | − | 0.994837i | \(-0.532360\pi\) |
−0.912298 | + | 0.409527i | \(0.865694\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.21948 | + | 1.85877i | −0.283459 | + | 0.163655i | ||||
\(130\) | 3.30030 | + | 6.32495i | 0.289455 | + | 0.554735i | ||||
\(131\) | −9.50083 | − | 5.48531i | −0.830092 | − | 0.479254i | 0.0237925 | − | 0.999717i | \(-0.492426\pi\) |
−0.853884 | + | 0.520463i | \(0.825759\pi\) | |||||||
\(132\) | 4.11264 | + | 2.37443i | 0.357959 | + | 0.206668i | ||||
\(133\) | 10.3029 | − | 17.8452i | 0.893378 | − | 1.54738i | ||||
\(134\) | − | 0.561100i | − | 0.0484717i | ||||||
\(135\) | −1.98242 | + | 1.03441i | −0.170620 | + | 0.0890278i | ||||
\(136\) | −2.99127 | + | 5.18104i | −0.256500 | + | 0.444270i | ||||
\(137\) | 6.13407i | 0.524069i | 0.965059 | + | 0.262034i | \(0.0843934\pi\) | ||||
−0.965059 | + | 0.262034i | \(0.915607\pi\) | |||||||
\(138\) | 2.02051i | 0.171997i | ||||||||
\(139\) | −8.14444 | + | 14.1066i | −0.690802 | + | 1.19650i | 0.280773 | + | 0.959774i | \(0.409409\pi\) |
−0.971575 | + | 0.236731i | \(0.923924\pi\) | |||||||
\(140\) | −0.349478 | + | 8.18506i | −0.0295363 | + | 0.691764i | ||||
\(141\) | 5.06368 | + | 8.77054i | 0.426438 | + | 0.738613i | ||||
\(142\) | 12.6344 | 1.06026 | ||||||||
\(143\) | −7.57566 | − | 13.1214i | −0.633508 | − | 1.09727i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −7.54802 | + | 3.93849i | −0.626829 | + | 0.327073i | ||||
\(146\) | 2.31646 | + | 1.33741i | 0.191712 | + | 0.110685i | ||||
\(147\) | 6.42347i | 0.529799i | ||||||||
\(148\) | −1.36779 | − | 5.92699i | −0.112431 | − | 0.487195i | ||||
\(149\) | 10.4656 | 0.857375 | 0.428688 | − | 0.903453i | \(-0.358976\pi\) | ||||
0.428688 | + | 0.903453i | \(0.358976\pi\) | |||||||
\(150\) | 4.10127 | + | 2.86000i | 0.334867 | + | 0.233518i | ||||
\(151\) | 1.36743 | + | 2.36845i | 0.111280 | + | 0.192742i | 0.916286 | − | 0.400524i | \(-0.131172\pi\) |
−0.805007 | + | 0.593266i | \(0.797838\pi\) | |||||||
\(152\) | −4.87068 | + | 2.81209i | −0.395064 | + | 0.228090i | ||||
\(153\) | 2.99127 | + | 5.18104i | 0.241830 | + | 0.418862i | ||||
\(154\) | − | 17.3989i | − | 1.40204i | ||||||
\(155\) | 12.6621 | − | 6.60695i | 1.01704 | − | 0.530683i | ||||
\(156\) | − | 3.19052i | − | 0.255446i | ||||||
\(157\) | 8.43062 | + | 4.86742i | 0.672837 | + | 0.388462i | 0.797151 | − | 0.603781i | \(-0.206340\pi\) |
−0.124314 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(158\) | 1.91176i | 0.152091i | ||||||||
\(159\) | 7.61652 | 0.604029 | ||||||||
\(160\) | 1.19962 | − | 1.88704i | 0.0948386 | − | 0.149183i | ||||
\(161\) | 6.41096 | − | 3.70137i | 0.505255 | − | 0.291709i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.42804 | + | 7.66959i | −0.346831 | + | 0.600728i | −0.985685 | − | 0.168600i | \(-0.946075\pi\) |
0.638854 | + | 0.769328i | \(0.279409\pi\) | |||||||
\(164\) | 0.175565 | − | 0.304088i | 0.0137093 | − | 0.0237453i | ||||
\(165\) | −8.96127 | − | 5.69685i | −0.697634 | − | 0.443499i | ||||
\(166\) | 4.66513 | − | 2.69342i | 0.362085 | − | 0.209050i | ||||
\(167\) | 0.842814 | + | 1.45980i | 0.0652189 | + | 0.112962i | 0.896791 | − | 0.442454i | \(-0.145892\pi\) |
−0.831572 | + | 0.555417i | \(0.812559\pi\) | |||||||
\(168\) | 1.83190 | − | 3.17295i | 0.141334 | − | 0.244798i | ||||
\(169\) | 1.41031 | − | 2.44272i | 0.108485 | − | 0.187902i | ||||
\(170\) | 7.17680 | − | 11.2893i | 0.550436 | − | 0.865848i | ||||
\(171\) | 5.62418i | 0.430092i | ||||||||
\(172\) | −1.85877 | − | 3.21948i | −0.141730 | − | 0.245483i | ||||
\(173\) | 2.61050 | + | 1.50717i | 0.198473 | + | 0.114588i | 0.595943 | − | 0.803027i | \(-0.296778\pi\) |
−0.397470 | + | 0.917615i | \(0.630112\pi\) | |||||||
\(174\) | 3.80747 | 0.288644 | ||||||||
\(175\) | 1.56149 | − | 18.2524i | 0.118037 | − | 1.37975i | ||||
\(176\) | −2.37443 | + | 4.11264i | −0.178979 | + | 0.310002i | ||||
\(177\) | 10.0964 | 0.758889 | ||||||||
\(178\) | −10.8009 | + | 6.23589i | −0.809560 | + | 0.467400i | ||||
\(179\) | 15.9241i | 1.19022i | 0.803643 | + | 0.595112i | \(0.202892\pi\) | ||||
−0.803643 | + | 0.595112i | \(0.797108\pi\) | |||||||
\(180\) | −1.03441 | − | 1.98242i | −0.0771003 | − | 0.147761i | ||||
\(181\) | 7.78303 | + | 13.4806i | 0.578508 | + | 1.00201i | 0.995651 | + | 0.0931645i | \(0.0296982\pi\) |
−0.417143 | + | 0.908841i | \(0.636968\pi\) | |||||||
\(182\) | −10.1233 | + | 5.84471i | −0.750392 | + | 0.433239i | ||||
\(183\) | 7.68125 | − | 13.3043i | 0.567814 | − | 0.983483i | ||||
\(184\) | −2.02051 | −0.148954 | ||||||||
\(185\) | 2.49032 | + | 13.3715i | 0.183092 | + | 0.983096i | ||||
\(186\) | −6.38718 | −0.468330 | ||||||||
\(187\) | −14.2051 | + | 24.6040i | −1.03878 | + | 1.79922i | ||||
\(188\) | −8.77054 | + | 5.06368i | −0.639658 | + | 0.369306i | ||||
\(189\) | −1.83190 | − | 3.17295i | −0.133251 | − | 0.230798i | ||||
\(190\) | 11.1495 | − | 5.81770i | 0.808869 | − | 0.422060i | ||||
\(191\) | 24.7512i | 1.79094i | 0.445125 | + | 0.895469i | \(0.353159\pi\) | ||||
−0.445125 | + | 0.895469i | \(0.646841\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 1.35323 | 0.0974077 | 0.0487038 | − | 0.998813i | \(-0.484491\pi\) | ||||
0.0487038 | + | 0.998813i | \(0.484491\pi\) | |||||||
\(194\) | 1.53773 | − | 2.66342i | 0.110402 | − | 0.191223i | ||||
\(195\) | −0.304332 | + | 7.12771i | −0.0217937 | + | 0.510426i | ||||
\(196\) | −6.42347 | −0.458819 | ||||||||
\(197\) | 11.5053 | + | 6.64261i | 0.819721 | + | 0.473266i | 0.850320 | − | 0.526266i | \(-0.176408\pi\) |
−0.0305992 | + | 0.999532i | \(0.509742\pi\) | |||||||
\(198\) | 2.37443 | + | 4.11264i | 0.168743 | + | 0.292272i | ||||
\(199\) | 2.69300i | 0.190902i | 0.995434 | + | 0.0954509i | \(0.0304293\pi\) | ||||
−0.995434 | + | 0.0954509i | \(0.969571\pi\) | |||||||
\(200\) | −2.86000 | + | 4.10127i | −0.202232 | + | 0.290004i | ||||
\(201\) | 0.280550 | − | 0.485927i | 0.0197885 | − | 0.0342746i | ||||
\(202\) | −1.94064 | + | 3.36129i | −0.136543 | + | 0.236499i | ||||
\(203\) | −6.97492 | − | 12.0809i | −0.489544 | − | 0.847914i | ||||
\(204\) | −5.18104 | + | 2.99127i | −0.362745 | + | 0.209431i | ||||
\(205\) | −0.421224 | + | 0.662595i | −0.0294196 | + | 0.0462777i | ||||
\(206\) | 0.265071 | − | 0.459116i | 0.0184684 | − | 0.0319881i | ||||
\(207\) | −1.01025 | + | 1.74981i | −0.0702174 | + | 0.121620i | ||||
\(208\) | 3.19052 | 0.221222 | ||||||||
\(209\) | −23.1302 | + | 13.3542i | −1.59995 | + | 0.923731i | ||||
\(210\) | −4.39519 | + | 6.91373i | −0.303297 | + | 0.477093i | ||||
\(211\) | 2.39058 | 0.164575 | 0.0822873 | − | 0.996609i | \(-0.473777\pi\) | ||||
0.0822873 | + | 0.996609i | \(0.473777\pi\) | |||||||
\(212\) | 7.61652i | 0.523105i | ||||||||
\(213\) | 10.9417 | + | 6.31722i | 0.749716 | + | 0.432849i | ||||
\(214\) | − | 10.8930i | − | 0.744633i | ||||||
\(215\) | 3.84545 | + | 7.36972i | 0.262257 | + | 0.502611i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 11.7007 | + | 20.2662i | 0.794294 | + | 1.37576i | ||||
\(218\) | −4.73143 | + | 2.73169i | −0.320453 | + | 0.185013i | ||||
\(219\) | 1.33741 | + | 2.31646i | 0.0903739 | + | 0.156532i | ||||
\(220\) | 5.69685 | − | 8.96127i | 0.384081 | − | 0.604169i | ||||
\(221\) | 19.0874 | 1.28396 | ||||||||
\(222\) | 1.77896 | − | 5.81681i | 0.119396 | − | 0.390399i | ||||
\(223\) | − | 8.66496i | − | 0.580249i | −0.956989 | − | 0.290124i | \(-0.906303\pi\) | ||
0.956989 | − | 0.290124i | \(-0.0936966\pi\) | |||||||
\(224\) | 3.17295 | + | 1.83190i | 0.212002 | + | 0.122399i | ||||
\(225\) | 2.12181 | + | 4.52746i | 0.141454 | + | 0.301831i | ||||
\(226\) | 5.15391 | + | 8.92683i | 0.342833 | + | 0.593804i | ||||
\(227\) | −6.39535 | − | 11.0771i | −0.424474 | − | 0.735211i | 0.571897 | − | 0.820326i | \(-0.306208\pi\) |
−0.996371 | + | 0.0851142i | \(0.972874\pi\) | |||||||
\(228\) | −5.62418 | −0.372470 | ||||||||
\(229\) | −7.44705 | − | 12.8987i | −0.492115 | − | 0.852368i | 0.507844 | − | 0.861449i | \(-0.330443\pi\) |
−0.999959 | + | 0.00908146i | \(0.997109\pi\) | |||||||
\(230\) | 4.51388 | + | 0.192729i | 0.297636 | + | 0.0127082i | ||||
\(231\) | 8.69945 | − | 15.0679i | 0.572382 | − | 0.991395i | ||||
\(232\) | 3.80747i | 0.249973i | ||||||||
\(233\) | 25.2493i | 1.65414i | 0.562103 | + | 0.827068i | \(0.309993\pi\) | ||||
−0.562103 | + | 0.827068i | \(0.690007\pi\) | |||||||
\(234\) | 1.59526 | − | 2.76307i | 0.104285 | − | 0.180627i | ||||
\(235\) | 20.0767 | − | 10.4758i | 1.30966 | − | 0.683367i | ||||
\(236\) | 10.0964i | 0.657217i | ||||||||
\(237\) | −0.955880 | + | 1.65563i | −0.0620911 | + | 0.107545i | ||||
\(238\) | 18.9823 | + | 10.9594i | 1.23044 | + | 0.710395i | ||||
\(239\) | 25.7697 | + | 14.8781i | 1.66690 | + | 0.962386i | 0.969293 | + | 0.245907i | \(0.0790858\pi\) |
0.697608 | + | 0.716479i | \(0.254248\pi\) | |||||||
\(240\) | 1.98242 | − | 1.03441i | 0.127965 | − | 0.0667708i | ||||
\(241\) | −18.8752 | + | 10.8976i | −1.21586 | + | 0.701978i | −0.964030 | − | 0.265793i | \(-0.914366\pi\) |
−0.251831 | + | 0.967771i | \(0.581033\pi\) | |||||||
\(242\) | −5.77585 | + | 10.0041i | −0.371286 | + | 0.643086i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 13.3043 | + | 7.68125i | 0.851721 | + | 0.491741i | ||||
\(245\) | 14.3502 | + | 0.612712i | 0.916803 | + | 0.0391448i | ||||
\(246\) | 0.304088 | − | 0.175565i | 0.0193879 | − | 0.0111936i | ||||
\(247\) | 15.5400 | + | 8.97201i | 0.988785 | + | 0.570875i | ||||
\(248\) | − | 6.38718i | − | 0.405586i | ||||||
\(249\) | 5.38683 | 0.341377 | ||||||||
\(250\) | 6.78053 | − | 8.88957i | 0.428838 | − | 0.562226i | ||||
\(251\) | − | 19.4874i | − | 1.23003i | −0.788514 | − | 0.615017i | \(-0.789149\pi\) | ||
0.788514 | − | 0.615017i | \(-0.210851\pi\) | |||||||
\(252\) | 3.17295 | − | 1.83190i | 0.199877 | − | 0.115399i | ||||
\(253\) | −9.59511 | −0.603239 | ||||||||
\(254\) | 11.4248 | − | 6.59611i | 0.716855 | − | 0.413877i | ||||
\(255\) | 11.8599 | − | 6.18840i | 0.742698 | − | 0.387533i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −15.5721 | + | 26.9717i | −0.971363 | + | 1.68245i | −0.279913 | + | 0.960025i | \(0.590306\pi\) |
−0.691450 | + | 0.722425i | \(0.743028\pi\) | |||||||
\(258\) | − | 3.71753i | − | 0.231443i | ||||||
\(259\) | −21.7153 | + | 5.01130i | −1.34932 | + | 0.311387i | ||||
\(260\) | −7.12771 | − | 0.304332i | −0.442042 | − | 0.0188739i | ||||
\(261\) | 3.29737 | + | 1.90374i | 0.204102 | + | 0.117838i | ||||
\(262\) | 9.50083 | − | 5.48531i | 0.586963 | − | 0.338883i | ||||
\(263\) | −1.99559 | + | 1.15216i | −0.123053 | + | 0.0710449i | −0.560263 | − | 0.828315i | \(-0.689300\pi\) |
0.437210 | + | 0.899360i | \(0.355967\pi\) | |||||||
\(264\) | −4.11264 | + | 2.37443i | −0.253115 | + | 0.146136i | ||||
\(265\) | 0.726513 | − | 17.0156i | 0.0446294 | − | 1.04526i | ||||
\(266\) | 10.3029 | + | 17.8452i | 0.631714 | + | 1.09416i | ||||
\(267\) | −12.4718 | −0.763261 | ||||||||
\(268\) | 0.485927 | + | 0.280550i | 0.0296827 | + | 0.0171373i | ||||
\(269\) | 18.0246 | 1.09898 | 0.549491 | − | 0.835500i | \(-0.314822\pi\) | ||||
0.549491 | + | 0.835500i | \(0.314822\pi\) | |||||||
\(270\) | 0.0953865 | − | 2.23403i | 0.00580504 | − | 0.135959i | ||||
\(271\) | −14.7396 | + | 25.5297i | −0.895365 | + | 1.55082i | −0.0620119 | + | 0.998075i | \(0.519752\pi\) |
−0.833353 | + | 0.552742i | \(0.813582\pi\) | |||||||
\(272\) | −2.99127 | − | 5.18104i | −0.181373 | − | 0.314146i | ||||
\(273\) | −11.6894 | −0.707476 | ||||||||
\(274\) | −5.31226 | − | 3.06703i | −0.320925 | − | 0.185286i | ||||
\(275\) | −13.5817 | + | 19.4764i | −0.819009 | + | 1.17447i | ||||
\(276\) | −1.74981 | − | 1.01025i | −0.105326 | − | 0.0608101i | ||||
\(277\) | 1.97273 | + | 3.41686i | 0.118530 | + | 0.205299i | 0.919185 | − | 0.393826i | \(-0.128849\pi\) |
−0.800656 | + | 0.599125i | \(0.795515\pi\) | |||||||
\(278\) | −8.14444 | − | 14.1066i | −0.488471 | − | 0.846057i | ||||
\(279\) | −5.53146 | − | 3.19359i | −0.331160 | − | 0.191195i | ||||
\(280\) | −6.91373 | − | 4.39519i | −0.413174 | − | 0.262663i | ||||
\(281\) | −27.7360 | − | 16.0134i | −1.65459 | − | 0.955279i | −0.975149 | − | 0.221549i | \(-0.928889\pi\) |
−0.679442 | − | 0.733729i | \(-0.737778\pi\) | |||||||
\(282\) | −10.1274 | −0.603075 | ||||||||
\(283\) | 2.97713 | + | 5.15654i | 0.176972 | + | 0.306524i | 0.940842 | − | 0.338846i | \(-0.110036\pi\) |
−0.763870 | + | 0.645370i | \(0.776703\pi\) | |||||||
\(284\) | −6.31722 | + | 10.9417i | −0.374858 | + | 0.649273i | ||||
\(285\) | 12.5646 | + | 0.536471i | 0.744262 | + | 0.0317778i | ||||
\(286\) | 15.1513 | 0.895916 | ||||||||
\(287\) | −1.11412 | − | 0.643236i | −0.0657643 | − | 0.0379690i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.39542 | − | 16.2733i | −0.552672 | − | 0.957256i | ||||
\(290\) | 0.363182 | − | 8.50602i | 0.0213268 | − | 0.499491i | ||||
\(291\) | 2.66342 | − | 1.53773i | 0.156133 | − | 0.0901432i | ||||
\(292\) | −2.31646 | + | 1.33741i | −0.135561 | + | 0.0782661i | ||||
\(293\) | 14.2855 | − | 8.24771i | 0.834565 | − | 0.481836i | −0.0208481 | − | 0.999783i | \(-0.506637\pi\) |
0.855413 | + | 0.517946i | \(0.173303\pi\) | |||||||
\(294\) | −5.56289 | − | 3.21173i | −0.324434 | − | 0.187312i | ||||
\(295\) | 0.963057 | − | 22.5556i | 0.0560714 | − | 1.31324i | ||||
\(296\) | 5.81681 | + | 1.77896i | 0.338095 | + | 0.103400i | ||||
\(297\) | 4.74886i | 0.275557i | ||||||||
\(298\) | −5.23280 | + | 9.06348i | −0.303128 | + | 0.525033i | ||||
\(299\) | 3.22323 | + | 5.58279i | 0.186404 | + | 0.322861i | ||||
\(300\) | −4.52746 | + | 2.12181i | −0.261393 | + | 0.122503i | ||||
\(301\) | −11.7955 | + | 6.81016i | −0.679883 | + | 0.392531i | ||||
\(302\) | −2.73485 | −0.157373 | ||||||||
\(303\) | −3.36129 | + | 1.94064i | −0.193101 | + | 0.111487i | ||||
\(304\) | − | 5.62418i | − | 0.322569i | ||||||
\(305\) | −28.9896 | − | 18.4292i | −1.65994 | − | 1.05525i | ||||
\(306\) | −5.98255 | −0.341999 | ||||||||
\(307\) | 9.90534i | 0.565327i | 0.959219 | + | 0.282664i | \(0.0912180\pi\) | ||||
−0.959219 | + | 0.282664i | \(0.908782\pi\) | |||||||
\(308\) | 15.0679 | + | 8.69945i | 0.858573 | + | 0.495697i | ||||
\(309\) | 0.459116 | − | 0.265071i | 0.0261182 | − | 0.0150794i | ||||
\(310\) | −0.609251 | + | 14.2692i | −0.0346031 | + | 0.810434i | ||||
\(311\) | −11.4094 | − | 6.58725i | −0.646971 | − | 0.373529i | 0.140324 | − | 0.990106i | \(-0.455186\pi\) |
−0.787295 | + | 0.616577i | \(0.788519\pi\) | |||||||
\(312\) | 2.76307 | + | 1.59526i | 0.156428 | + | 0.0903137i | ||||
\(313\) | −13.1181 | + | 22.7212i | −0.741478 | + | 1.28428i | 0.210345 | + | 0.977627i | \(0.432541\pi\) |
−0.951822 | + | 0.306650i | \(0.900792\pi\) | |||||||
\(314\) | −8.43062 | + | 4.86742i | −0.475767 | + | 0.274684i | ||||
\(315\) | −7.26321 | + | 3.78987i | −0.409235 | + | 0.213535i | ||||
\(316\) | −1.65563 | − | 0.955880i | −0.0931366 | − | 0.0537724i | ||||
\(317\) | −16.8690 | − | 9.73933i | −0.947458 | − | 0.547015i | −0.0551676 | − | 0.998477i | \(-0.517569\pi\) |
−0.892290 | + | 0.451462i | \(0.850903\pi\) | |||||||
\(318\) | −3.80826 | + | 6.59610i | −0.213557 | + | 0.369891i | ||||
\(319\) | 18.0812i | 1.01235i | ||||||||
\(320\) | 1.03441 | + | 1.98242i | 0.0578252 | + | 0.110821i | ||||
\(321\) | 5.44652 | − | 9.43365i | 0.303995 | − | 0.526535i | ||||
\(322\) | 7.40274i | 0.412539i | ||||||||
\(323\) | − | 33.6469i | − | 1.87216i | ||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 15.8945 | + | 1.35978i | 0.881669 | + | 0.0754268i | ||||
\(326\) | −4.42804 | − | 7.66959i | −0.245246 | − | 0.424779i | ||||
\(327\) | −5.46338 | −0.302126 | ||||||||
\(328\) | 0.175565 | + | 0.304088i | 0.00969396 | + | 0.0167904i | ||||
\(329\) | 18.5523 | + | 32.1336i | 1.02282 | + | 1.77158i | ||||
\(330\) | 9.41425 | − | 4.91227i | 0.518237 | − | 0.270411i | ||||
\(331\) | 19.2273 | + | 11.1009i | 1.05683 | + | 0.610161i | 0.924554 | − | 0.381052i | \(-0.124438\pi\) |
0.132276 | + | 0.991213i | \(0.457771\pi\) | |||||||
\(332\) | 5.38683i | 0.295641i | ||||||||
\(333\) | 4.44903 | − | 4.14803i | 0.243805 | − | 0.227311i | ||||
\(334\) | −1.68563 | −0.0922334 | ||||||||
\(335\) | −1.05882 | − | 0.673109i | −0.0578493 | − | 0.0367759i | ||||
\(336\) | 1.83190 | + | 3.17295i | 0.0999385 | + | 0.173099i | ||||
\(337\) | −12.9418 | + | 7.47196i | −0.704985 | + | 0.407024i | −0.809202 | − | 0.587531i | \(-0.800100\pi\) |
0.104216 | + | 0.994555i | \(0.466767\pi\) | |||||||
\(338\) | 1.41031 | + | 2.44272i | 0.0767105 | + | 0.132867i | ||||
\(339\) | 10.3078i | 0.559844i | ||||||||
\(340\) | 6.18840 | + | 11.8599i | 0.335613 | + | 0.643195i | ||||
\(341\) | − | 30.3318i | − | 1.64256i | ||||||
\(342\) | −4.87068 | − | 2.81209i | −0.263376 | − | 0.152060i | ||||
\(343\) | − | 2.11230i | − | 0.114054i | ||||||
\(344\) | 3.71753 | 0.200436 | ||||||||
\(345\) | 3.81277 | + | 2.42385i | 0.205272 | + | 0.130496i | ||||
\(346\) | −2.61050 | + | 1.50717i | −0.140341 | + | 0.0810261i | ||||
\(347\) | −24.5558 | −1.31823 | −0.659113 | − | 0.752044i | \(-0.729068\pi\) | ||||
−0.659113 | + | 0.752044i | \(0.729068\pi\) | |||||||
\(348\) | −1.90374 | + | 3.29737i | −0.102051 | + | 0.176758i | ||||
\(349\) | −5.68801 | + | 9.85192i | −0.304472 | + | 0.527361i | −0.977144 | − | 0.212580i | \(-0.931813\pi\) |
0.672671 | + | 0.739941i | \(0.265147\pi\) | |||||||
\(350\) | 15.0263 | + | 10.4785i | 0.803187 | + | 0.560098i | ||||
\(351\) | 2.76307 | − | 1.59526i | 0.147482 | − | 0.0851486i | ||||
\(352\) | −2.37443 | − | 4.11264i | −0.126558 | − | 0.219204i | ||||
\(353\) | 3.82580 | − | 6.62648i | 0.203627 | − | 0.352692i | −0.746067 | − | 0.665870i | \(-0.768060\pi\) |
0.949694 | + | 0.313178i | \(0.101394\pi\) | |||||||
\(354\) | −5.04818 | + | 8.74371i | −0.268308 | + | 0.464723i | ||||
\(355\) | 15.1566 | − | 23.8416i | 0.804427 | − | 1.26538i | ||||
\(356\) | − | 12.4718i | − | 0.661003i | ||||||
\(357\) | 10.9594 | + | 18.9823i | 0.580035 | + | 1.00465i | ||||
\(358\) | −13.7907 | − | 7.96205i | −0.728860 | − | 0.420807i | ||||
\(359\) | 15.6117 | 0.823952 | 0.411976 | − | 0.911195i | \(-0.364839\pi\) | ||||
0.411976 | + | 0.911195i | \(0.364839\pi\) | |||||||
\(360\) | 2.23403 | + | 0.0953865i | 0.117744 | + | 0.00502731i | ||||
\(361\) | 6.31568 | − | 10.9391i | 0.332404 | − | 0.575741i | ||||
\(362\) | −15.5661 | −0.818134 | ||||||||
\(363\) | −10.0041 | + | 5.77585i | −0.525077 | + | 0.303153i | ||||
\(364\) | − | 11.6894i | − | 0.612692i | ||||||
\(365\) | 5.30263 | − | 2.76686i | 0.277552 | − | 0.144824i | ||||
\(366\) | 7.68125 | + | 13.3043i | 0.401505 | + | 0.695427i | ||||
\(367\) | −15.2460 | + | 8.80231i | −0.795837 | + | 0.459477i | −0.842013 | − | 0.539457i | \(-0.818630\pi\) |
0.0461764 | + | 0.998933i | \(0.485296\pi\) | |||||||
\(368\) | 1.01025 | − | 1.74981i | 0.0526631 | − | 0.0912151i | ||||
\(369\) | 0.351130 | 0.0182791 | ||||||||
\(370\) | −12.8253 | − | 4.52909i | −0.666754 | − | 0.235456i | ||||
\(371\) | 27.9054 | 1.44878 | ||||||||
\(372\) | 3.19359 | − | 5.53146i | 0.165580 | − | 0.286793i | ||||
\(373\) | 27.8407 | − | 16.0738i | 1.44154 | − | 0.832272i | 0.443584 | − | 0.896233i | \(-0.353707\pi\) |
0.997952 | + | 0.0639612i | \(0.0203734\pi\) | |||||||
\(374\) | −14.2051 | − | 24.6040i | −0.734530 | − | 1.27224i | ||||
\(375\) | 10.3169 | − | 4.30833i | 0.532762 | − | 0.222481i | ||||
\(376\) | − | 10.1274i | − | 0.522278i | ||||||
\(377\) | 10.5203 | − | 6.07390i | 0.541823 | − | 0.312822i | ||||
\(378\) | 3.66381 | 0.188446 | ||||||||
\(379\) | 1.28515 | − | 2.22595i | 0.0660138 | − | 0.114339i | −0.831129 | − | 0.556079i | \(-0.812305\pi\) |
0.897143 | + | 0.441740i | \(0.145639\pi\) | |||||||
\(380\) | −0.536471 | + | 12.5646i | −0.0275204 | + | 0.644550i | ||||
\(381\) | 13.1922 | 0.675858 | ||||||||
\(382\) | −21.4352 | − | 12.3756i | −1.09672 | − | 0.633192i | ||||
\(383\) | 9.81643 | + | 17.0025i | 0.501596 | + | 0.868790i | 0.999998 | + | 0.00184377i | \(0.000586889\pi\) |
−0.498402 | + | 0.866946i | \(0.666080\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −32.8324 | − | 20.8721i | −1.67329 | − | 1.06374i | ||||
\(386\) | −0.676615 | + | 1.17193i | −0.0344388 | + | 0.0596498i | ||||
\(387\) | 1.85877 | − | 3.21948i | 0.0944864 | − | 0.163655i | ||||
\(388\) | 1.53773 | + | 2.66342i | 0.0780663 | + | 0.135215i | ||||
\(389\) | −18.7903 | + | 10.8486i | −0.952707 | + | 0.550046i | −0.893921 | − | 0.448225i | \(-0.852056\pi\) |
−0.0587865 | + | 0.998271i | \(0.518723\pi\) | |||||||
\(390\) | −6.02062 | − | 3.82742i | −0.304866 | − | 0.193809i | ||||
\(391\) | 6.04388 | − | 10.4683i | 0.305652 | − | 0.529405i | ||||
\(392\) | 3.21173 | − | 5.56289i | 0.162217 | − | 0.280968i | ||||
\(393\) | 10.9706 | 0.553394 | ||||||||
\(394\) | −11.5053 | + | 6.64261i | −0.579630 | + | 0.334650i | ||||
\(395\) | 3.60756 | + | 2.29339i | 0.181516 | + | 0.115393i | ||||
\(396\) | −4.74886 | −0.238639 | ||||||||
\(397\) | − | 14.8755i | − | 0.746580i | −0.927715 | − | 0.373290i | \(-0.878230\pi\) | ||
0.927715 | − | 0.373290i | \(-0.121770\pi\) | |||||||
\(398\) | −2.33221 | − | 1.34650i | −0.116903 | − | 0.0674940i | ||||
\(399\) | 20.6059i | 1.03158i | ||||||||
\(400\) | −2.12181 | − | 4.52746i | −0.106090 | − | 0.226373i | ||||
\(401\) | − | 9.50343i | − | 0.474578i | −0.971439 | − | 0.237289i | \(-0.923741\pi\) | ||
0.971439 | − | 0.237289i | \(-0.0762589\pi\) | |||||||
\(402\) | 0.280550 | + | 0.485927i | 0.0139926 | + | 0.0242358i | ||||
\(403\) | −17.6482 | + | 10.1892i | −0.879119 | + | 0.507560i | ||||
\(404\) | −1.94064 | − | 3.36129i | −0.0965504 | − | 0.167230i | ||||
\(405\) | 1.19962 | − | 1.88704i | 0.0596098 | − | 0.0937676i | ||||
\(406\) | 13.9498 | 0.692319 | ||||||||
\(407\) | 27.6232 | + | 8.44801i | 1.36923 | + | 0.418752i | ||||
\(408\) | − | 5.98255i | − | 0.296180i | ||||||
\(409\) | 8.91611 | + | 5.14772i | 0.440873 | + | 0.254538i | 0.703968 | − | 0.710232i | \(-0.251410\pi\) |
−0.263095 | + | 0.964770i | \(0.584743\pi\) | |||||||
\(410\) | −0.363212 | − | 0.696088i | −0.0179378 | − | 0.0343774i | ||||
\(411\) | −3.06703 | − | 5.31226i | −0.151286 | − | 0.262034i | ||||
\(412\) | 0.265071 | + | 0.459116i | 0.0130591 | + | 0.0226190i | ||||
\(413\) | 36.9911 | 1.82021 | ||||||||
\(414\) | −1.01025 | − | 1.74981i | −0.0496512 | − | 0.0859984i | ||||
\(415\) | 0.513831 | − | 12.0344i | 0.0252230 | − | 0.590743i | ||||
\(416\) | −1.59526 | + | 2.76307i | −0.0782139 | + | 0.135471i | ||||
\(417\) | − | 16.2889i | − | 0.797670i | ||||||
\(418\) | − | 26.7084i | − | 1.30635i | ||||||
\(419\) | −1.35626 | + | 2.34912i | −0.0662578 | + | 0.114762i | −0.897251 | − | 0.441520i | \(-0.854439\pi\) |
0.830993 | + | 0.556282i | \(0.187773\pi\) | |||||||
\(420\) | −3.78987 | − | 7.26321i | −0.184927 | − | 0.354408i | ||||
\(421\) | 39.3859i | 1.91955i | 0.280770 | + | 0.959775i | \(0.409410\pi\) | ||||
−0.280770 | + | 0.959775i | \(0.590590\pi\) | |||||||
\(422\) | −1.19529 | + | 2.07031i | −0.0581859 | + | 0.100781i | ||||
\(423\) | −8.77054 | − | 5.06368i | −0.426438 | − | 0.246204i | ||||
\(424\) | −6.59610 | − | 3.80826i | −0.320335 | − | 0.184945i | ||||
\(425\) | −12.6938 | − | 27.0858i | −0.615740 | − | 1.31385i | ||||
\(426\) | −10.9417 | + | 6.31722i | −0.530129 | + | 0.306070i | ||||
\(427\) | 28.1426 | − | 48.7444i | 1.36192 | − | 2.35891i | ||||
\(428\) | 9.43365 | + | 5.44652i | 0.455993 | + | 0.263268i | ||||
\(429\) | 13.1214 | + | 7.57566i | 0.633508 | + | 0.365756i | ||||
\(430\) | −8.30509 | − | 0.354602i | −0.400507 | − | 0.0171004i | ||||
\(431\) | 19.7864 | − | 11.4237i | 0.953079 | − | 0.550260i | 0.0590430 | − | 0.998255i | \(-0.481195\pi\) |
0.894036 | + | 0.447995i | \(0.147862\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 11.6308i | − | 0.558941i | −0.960154 | − | 0.279471i | \(-0.909841\pi\) | ||
0.960154 | − | 0.279471i | \(-0.0901589\pi\) | |||||||
\(434\) | −23.4014 | −1.12330 | ||||||||
\(435\) | 4.56754 | − | 7.18484i | 0.218997 | − | 0.344487i | ||||
\(436\) | − | 5.46338i | − | 0.261648i | ||||||
\(437\) | 9.84124 | − | 5.68184i | 0.470770 | − | 0.271799i | ||||
\(438\) | −2.67482 | −0.127808 | ||||||||
\(439\) | 16.2743 | − | 9.39600i | 0.776732 | − | 0.448447i | −0.0585387 | − | 0.998285i | \(-0.518644\pi\) |
0.835271 | + | 0.549839i | \(0.185311\pi\) | |||||||
\(440\) | 4.91227 | + | 9.41425i | 0.234183 | + | 0.448807i | ||||
\(441\) | −3.21173 | − | 5.56289i | −0.152940 | − | 0.264899i | ||||
\(442\) | −9.54370 | + | 16.5302i | −0.453948 | + | 0.786260i | ||||
\(443\) | 6.14048i | 0.291743i | 0.989304 | + | 0.145872i | \(0.0465986\pi\) | ||||
−0.989304 | + | 0.145872i | \(0.953401\pi\) | |||||||
\(444\) | 4.14803 | + | 4.44903i | 0.196857 | + | 0.211141i | ||||
\(445\) | −1.18964 | + | 27.8624i | −0.0563943 | + | 1.32080i | ||||
\(446\) | 7.50407 | + | 4.33248i | 0.355328 | + | 0.205149i | ||||
\(447\) | −9.06348 | + | 5.23280i | −0.428688 | + | 0.247503i | ||||
\(448\) | −3.17295 | + | 1.83190i | −0.149908 | + | 0.0865493i | ||||
\(449\) | −9.26368 | + | 5.34839i | −0.437180 | + | 0.252406i | −0.702401 | − | 0.711782i | \(-0.747889\pi\) |
0.265221 | + | 0.964188i | \(0.414555\pi\) | |||||||
\(450\) | −4.98180 | − | 0.426193i | −0.234844 | − | 0.0200909i | ||||
\(451\) | 0.833735 | + | 1.44407i | 0.0392590 | + | 0.0679986i | ||||
\(452\) | −10.3078 | −0.484839 | ||||||||
\(453\) | −2.36845 | − | 1.36743i | −0.111280 | − | 0.0642473i | ||||
\(454\) | 12.7907 | 0.600298 | ||||||||
\(455\) | −1.11501 | + | 26.1146i | −0.0522727 | + | 1.22427i | ||||
\(456\) | 2.81209 | − | 4.87068i | 0.131688 | − | 0.228090i | ||||
\(457\) | 18.8922 | + | 32.7222i | 0.883738 | + | 1.53068i | 0.847154 | + | 0.531348i | \(0.178314\pi\) |
0.0365837 | + | 0.999331i | \(0.488352\pi\) | |||||||
\(458\) | 14.8941 | 0.695955 | ||||||||
\(459\) | −5.18104 | − | 2.99127i | −0.241830 | − | 0.139621i | ||||
\(460\) | −2.42385 | + | 3.81277i | −0.113012 | + | 0.177771i | ||||
\(461\) | −30.1115 | − | 17.3849i | −1.40243 | − | 0.809693i | −0.407788 | − | 0.913076i | \(-0.633700\pi\) |
−0.994642 | + | 0.103383i | \(0.967033\pi\) | |||||||
\(462\) | 8.69945 | + | 15.0679i | 0.404735 | + | 0.701022i | ||||
\(463\) | 13.7935 | + | 23.8911i | 0.641039 | + | 1.11031i | 0.985201 | + | 0.171402i | \(0.0548297\pi\) |
−0.344162 | + | 0.938910i | \(0.611837\pi\) | |||||||
\(464\) | −3.29737 | − | 1.90374i | −0.153077 | − | 0.0883788i | ||||
\(465\) | −7.66221 | + | 12.0528i | −0.355326 | + | 0.558937i | ||||
\(466\) | −21.8665 | − | 12.6246i | −1.01295 | − | 0.584825i | ||||
\(467\) | 6.06099 | 0.280469 | 0.140235 | − | 0.990118i | \(-0.455214\pi\) | ||||
0.140235 | + | 0.990118i | \(0.455214\pi\) | |||||||
\(468\) | 1.59526 | + | 2.76307i | 0.0737408 | + | 0.127723i | ||||
\(469\) | 1.02788 | − | 1.78034i | 0.0474631 | − | 0.0822085i | ||||
\(470\) | −0.966013 | + | 22.6248i | −0.0445588 | + | 1.04361i | ||||
\(471\) | −9.73484 | −0.448558 | ||||||||
\(472\) | −8.74371 | − | 5.04818i | −0.402462 | − | 0.232361i | ||||
\(473\) | 17.6540 | 0.811734 | ||||||||
\(474\) | −0.955880 | − | 1.65563i | −0.0439050 | − | 0.0760457i | ||||
\(475\) | 2.39699 | − | 28.0185i | 0.109981 | − | 1.28558i | ||||
\(476\) | −18.9823 | + | 10.9594i | −0.870053 | + | 0.502325i | ||||
\(477\) | −6.59610 | + | 3.80826i | −0.302015 | + | 0.174368i | ||||
\(478\) | −25.7697 | + | 14.8781i | −1.17868 | + | 0.680510i | ||||
\(479\) | −23.5812 | − | 13.6146i | −1.07745 | − | 0.622068i | −0.147245 | − | 0.989100i | \(-0.547040\pi\) |
−0.930208 | + | 0.367032i | \(0.880374\pi\) | |||||||
\(480\) | −0.0953865 | + | 2.23403i | −0.00435378 | + | 0.101969i | ||||
\(481\) | −4.36394 | − | 18.9101i | −0.198979 | − | 0.862228i | ||||
\(482\) | − | 21.7953i | − | 0.992747i | ||||||
\(483\) | −3.70137 | + | 6.41096i | −0.168418 | + | 0.291709i | ||||
\(484\) | −5.77585 | − | 10.0041i | −0.262539 | − | 0.454730i | ||||
\(485\) | −3.18128 | − | 6.09685i | −0.144454 | − | 0.276844i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −16.4926 | −0.747350 | −0.373675 | − | 0.927560i | \(-0.621902\pi\) | ||||
−0.373675 | + | 0.927560i | \(0.621902\pi\) | |||||||
\(488\) | −13.3043 | + | 7.68125i | −0.602258 | + | 0.347714i | ||||
\(489\) | − | 8.85607i | − | 0.400486i | ||||||
\(490\) | −7.70574 | + | 12.1213i | −0.348110 | + | 0.547585i | ||||
\(491\) | 18.5050 | 0.835119 | 0.417559 | − | 0.908650i | \(-0.362886\pi\) | ||||
0.417559 | + | 0.908650i | \(0.362886\pi\) | |||||||
\(492\) | 0.351130i | 0.0158302i | ||||||||
\(493\) | −19.7267 | − | 11.3892i | −0.888444 | − | 0.512943i | ||||
\(494\) | −15.5400 | + | 8.97201i | −0.699177 | + | 0.403670i | ||||
\(495\) | 10.6091 | + | 0.452978i | 0.476844 | + | 0.0203598i | ||||
\(496\) | 5.53146 | + | 3.19359i | 0.248370 | + | 0.143396i | ||||
\(497\) | 40.0884 | + | 23.1451i | 1.79821 | + | 1.03820i | ||||
\(498\) | −2.69342 | + | 4.66513i | −0.120695 | + | 0.209050i | ||||
\(499\) | 22.8459 | − | 13.1901i | 1.02273 | − | 0.590471i | 0.107833 | − | 0.994169i | \(-0.465609\pi\) |
0.914892 | + | 0.403698i | \(0.132275\pi\) | |||||||
\(500\) | 4.30833 | + | 10.3169i | 0.192674 | + | 0.461386i | ||||
\(501\) | −1.45980 | − | 0.842814i | −0.0652189 | − | 0.0376541i | ||||
\(502\) | 16.8766 | + | 9.74370i | 0.753239 | + | 0.434883i | ||||
\(503\) | 17.0375 | − | 29.5098i | 0.759665 | − | 1.31578i | −0.183356 | − | 0.983047i | \(-0.558696\pi\) |
0.943021 | − | 0.332732i | \(-0.107971\pi\) | |||||||
\(504\) | 3.66381i | 0.163199i | ||||||||
\(505\) | 4.01483 | + | 7.69433i | 0.178658 | + | 0.342393i | ||||
\(506\) | 4.79755 | − | 8.30961i | 0.213277 | − | 0.369407i | ||||
\(507\) | 2.82061i | 0.125268i | ||||||||
\(508\) | 13.1922i | 0.585310i | ||||||||
\(509\) | 1.88097 | − | 3.25794i | 0.0833727 | − | 0.144406i | −0.821324 | − | 0.570462i | \(-0.806764\pi\) |
0.904697 | + | 0.426056i | \(0.140097\pi\) | |||||||
\(510\) | −0.570654 | + | 13.3652i | −0.0252690 | + | 0.591821i | ||||
\(511\) | 4.90001 | + | 8.48707i | 0.216764 | + | 0.375446i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.81209 | − | 4.87068i | −0.124157 | − | 0.215046i | ||||
\(514\) | −15.5721 | − | 26.9717i | −0.686857 | − | 1.18967i | ||||
\(515\) | −0.548384 | − | 1.05096i | −0.0241647 | − | 0.0463110i | ||||
\(516\) | 3.21948 | + | 1.85877i | 0.141730 | + | 0.0818276i | ||||
\(517\) | − | 48.0934i | − | 2.11515i | ||||||
\(518\) | 6.51774 | − | 21.3117i | 0.286373 | − | 0.936381i | ||||
\(519\) | −3.01434 | −0.132315 | ||||||||
\(520\) | 3.82742 | − | 6.02062i | 0.167843 | − | 0.264021i | ||||
\(521\) | −16.2245 | − | 28.1016i | −0.710807 | − | 1.23115i | −0.964555 | − | 0.263883i | \(-0.914997\pi\) |
0.253748 | − | 0.967270i | \(-0.418337\pi\) | |||||||
\(522\) | −3.29737 | + | 1.90374i | −0.144322 | + | 0.0833243i | ||||
\(523\) | 14.1760 | + | 24.5535i | 0.619871 | + | 1.07365i | 0.989509 | + | 0.144473i | \(0.0461486\pi\) |
−0.369637 | + | 0.929176i | \(0.620518\pi\) | |||||||
\(524\) | 10.9706i | 0.479254i | ||||||||
\(525\) | 7.77389 | + | 16.5877i | 0.339280 | + | 0.723949i | ||||
\(526\) | − | 2.30431i | − | 0.100473i | ||||||
\(527\) | 33.0922 | + | 19.1058i | 1.44152 | + | 0.832261i | ||||
\(528\) | − | 4.74886i | − | 0.206668i | ||||||
\(529\) | −18.9176 | −0.822502 | ||||||||
\(530\) | 14.3726 | + | 9.13696i | 0.624308 | + | 0.396884i | ||||
\(531\) | −8.74371 | + | 5.04818i | −0.379445 | + | 0.219072i | ||||
\(532\) | −20.6059 | −0.893378 | ||||||||
\(533\) | 0.560143 | − | 0.970197i | 0.0242625 | − | 0.0420239i | ||||
\(534\) | 6.23589 | − | 10.8009i | 0.269853 | − | 0.467400i | ||||
\(535\) | −20.5556 | − | 13.0676i | −0.888694 | − | 0.564959i | ||||
\(536\) | −0.485927 | + | 0.280550i | −0.0209888 | + | 0.0121179i | ||||
\(537\) | −7.96205 | − | 13.7907i | −0.343588 | − | 0.595112i | ||||
\(538\) | −9.01232 | + | 15.6098i | −0.388549 | + | 0.672986i | ||||
\(539\) | 15.2521 | − | 26.4174i | 0.656954 | − | 1.13788i | ||||
\(540\) | 1.88704 | + | 1.19962i | 0.0812051 | + | 0.0516236i | ||||
\(541\) | − | 16.5176i | − | 0.710146i | −0.934839 | − | 0.355073i | \(-0.884456\pi\) | ||
0.934839 | − | 0.355073i | \(-0.115544\pi\) | |||||||
\(542\) | −14.7396 | − | 25.5297i | −0.633118 | − | 1.09659i | ||||
\(543\) | −13.4806 | − | 7.78303i | −0.578508 | − | 0.334002i | ||||
\(544\) | 5.98255 | 0.256500 | ||||||||
\(545\) | −0.521133 | + | 12.2054i | −0.0223229 | + | 0.522821i | ||||
\(546\) | 5.84471 | − | 10.1233i | 0.250131 | − | 0.433239i | ||||
\(547\) | −29.1609 | −1.24683 | −0.623415 | − | 0.781891i | \(-0.714255\pi\) | ||||
−0.623415 | + | 0.781891i | \(0.714255\pi\) | |||||||
\(548\) | 5.31226 | − | 3.06703i | 0.226928 | − | 0.131017i | ||||
\(549\) | 15.3625i | 0.655655i | ||||||||
\(550\) | −10.0762 | − | 21.5003i | −0.429649 | − | 0.916776i | ||||
\(551\) | −10.7070 | − | 18.5450i | −0.456132 | − | 0.790043i | ||||
\(552\) | 1.74981 | − | 1.01025i | 0.0744768 | − | 0.0429992i | ||||
\(553\) | −3.50216 | + | 6.06591i | −0.148927 | + | 0.257949i | ||||
\(554\) | −3.94545 | −0.167626 | ||||||||
\(555\) | −8.84246 | − | 10.3349i | −0.375341 | − | 0.438694i | ||||
\(556\) | 16.2889 | 0.690802 | ||||||||
\(557\) | −5.11442 | + | 8.85844i | −0.216705 | + | 0.375344i | −0.953799 | − | 0.300447i | \(-0.902864\pi\) |
0.737094 | + | 0.675791i | \(0.236198\pi\) | |||||||
\(558\) | 5.53146 | − | 3.19359i | 0.234165 | − | 0.135195i | ||||
\(559\) | −5.93042 | − | 10.2718i | −0.250830 | − | 0.434450i | ||||
\(560\) | 7.26321 | − | 3.78987i | 0.306927 | − | 0.160151i | ||||
\(561\) | − | 28.4103i | − | 1.19948i | ||||||
\(562\) | 27.7360 | − | 16.0134i | 1.16997 | − | 0.675484i | ||||
\(563\) | 25.0290 | 1.05484 | 0.527422 | − | 0.849603i | \(-0.323159\pi\) | ||||
0.527422 | + | 0.849603i | \(0.323159\pi\) | |||||||
\(564\) | 5.06368 | − | 8.77054i | 0.213219 | − | 0.369306i | ||||
\(565\) | 23.0280 | + | 0.983227i | 0.968796 | + | 0.0413647i | ||||
\(566\) | −5.95426 | −0.250276 | ||||||||
\(567\) | 3.17295 | + | 1.83190i | 0.133251 | + | 0.0769327i | ||||
\(568\) | −6.31722 | − | 10.9417i | −0.265065 | − | 0.459105i | ||||
\(569\) | − | 2.35883i | − | 0.0988874i | −0.998777 | − | 0.0494437i | \(-0.984255\pi\) | ||
0.998777 | − | 0.0494437i | \(-0.0157448\pi\) | |||||||
\(570\) | −6.74689 | + | 10.6130i | −0.282596 | + | 0.444531i | ||||
\(571\) | −20.9518 | + | 36.2896i | −0.876807 | + | 1.51867i | −0.0219820 | + | 0.999758i | \(0.506998\pi\) |
−0.854825 | + | 0.518916i | \(0.826336\pi\) | |||||||
\(572\) | −7.57566 | + | 13.1214i | −0.316754 | + | 0.548634i | ||||
\(573\) | −12.3756 | − | 21.4352i | −0.516999 | − | 0.895469i | ||||
\(574\) | 1.11412 | − | 0.643236i | 0.0465024 | − | 0.0268482i | ||||
\(575\) | 5.77864 | − | 8.28664i | 0.240986 | − | 0.345577i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −19.2881 | + | 33.4079i | −0.802973 | + | 1.39079i | 0.114678 | + | 0.993403i | \(0.463416\pi\) |
−0.917651 | + | 0.397387i | \(0.869917\pi\) | |||||||
\(578\) | 18.7908 | 0.781596 | ||||||||
\(579\) | −1.17193 | + | 0.676615i | −0.0487038 | + | 0.0281192i | ||||
\(580\) | 7.18484 | + | 4.56754i | 0.298334 | + | 0.189657i | ||||
\(581\) | 19.7363 | 0.818800 | ||||||||
\(582\) | 3.07545i | 0.127482i | ||||||||
\(583\) | −31.3240 | − | 18.0849i | −1.29731 | − | 0.749000i | ||||
\(584\) | − | 2.67482i | − | 0.110685i | ||||||
\(585\) | −3.30030 | − | 6.32495i | −0.136451 | − | 0.261504i | ||||
\(586\) | 16.4954i | 0.681420i | ||||||||
\(587\) | −10.8364 | − | 18.7692i | −0.447266 | − | 0.774688i | 0.550941 | − | 0.834544i | \(-0.314269\pi\) |
−0.998207 | + | 0.0598566i | \(0.980936\pi\) | |||||||
\(588\) | 5.56289 | − | 3.21173i | 0.229410 | − | 0.132450i | ||||
\(589\) | 17.9613 | + | 31.1099i | 0.740083 | + | 1.28186i | ||||
\(590\) | 19.0522 | + | 12.1118i | 0.784367 | + | 0.498636i | ||||
\(591\) | −13.2852 | −0.546481 | ||||||||
\(592\) | −4.44903 | + | 4.14803i | −0.182854 | + | 0.170483i | ||||
\(593\) | 13.6002i | 0.558492i | 0.960220 | + | 0.279246i | \(0.0900844\pi\) | ||||
−0.960220 | + | 0.279246i | \(0.909916\pi\) | |||||||
\(594\) | −4.11264 | − | 2.37443i | −0.168743 | − | 0.0974241i | ||||
\(595\) | 43.4525 | − | 22.6731i | 1.78138 | − | 0.929506i | ||||
\(596\) | −5.23280 | − | 9.06348i | −0.214344 | − | 0.371254i | ||||
\(597\) | −1.34650 | − | 2.33221i | −0.0551086 | − | 0.0954509i | ||||
\(598\) | −6.44646 | −0.263615 | ||||||||
\(599\) | 11.8155 | + | 20.4651i | 0.482768 | + | 0.836179i | 0.999804 | − | 0.0197844i | \(-0.00629798\pi\) |
−0.517036 | + | 0.855964i | \(0.672965\pi\) | |||||||
\(600\) | 0.426193 | − | 4.98180i | 0.0173993 | − | 0.203381i | ||||
\(601\) | −7.39428 | + | 12.8073i | −0.301619 | + | 0.522420i | −0.976503 | − | 0.215504i | \(-0.930860\pi\) |
0.674884 | + | 0.737924i | \(0.264194\pi\) | |||||||
\(602\) | − | 13.6203i | − | 0.555122i | ||||||
\(603\) | 0.561100i | 0.0228498i | ||||||||
\(604\) | 1.36743 | − | 2.36845i | 0.0556398 | − | 0.0963710i | ||||
\(605\) | 11.9492 | + | 22.9003i | 0.485803 | + | 0.931031i | ||||
\(606\) | − | 3.88128i | − | 0.157666i | ||||||
\(607\) | 19.0358 | − | 32.9710i | 0.772639 | − | 1.33825i | −0.163472 | − | 0.986548i | \(-0.552269\pi\) |
0.936112 | − | 0.351703i | \(-0.114397\pi\) | |||||||
\(608\) | 4.87068 | + | 2.81209i | 0.197532 | + | 0.114045i | ||||
\(609\) | 12.0809 | + | 6.97492i | 0.489544 | + | 0.282638i | ||||
\(610\) | 30.4549 | − | 15.8911i | 1.23308 | − | 0.643412i | ||||
\(611\) | −27.9825 | + | 16.1557i | −1.13205 | + | 0.653591i | ||||
\(612\) | 2.99127 | − | 5.18104i | 0.120915 | − | 0.209431i | ||||
\(613\) | 41.1280 | + | 23.7453i | 1.66114 | + | 0.959062i | 0.972170 | + | 0.234276i | \(0.0752720\pi\) |
0.688974 | + | 0.724786i | \(0.258061\pi\) | |||||||
\(614\) | −8.57827 | − | 4.95267i | −0.346191 | − | 0.199873i | ||||
\(615\) | 0.0334931 | − | 0.784436i | 0.00135057 | − | 0.0316315i | ||||
\(616\) | −15.0679 | + | 8.69945i | −0.607103 | + | 0.350511i | ||||
\(617\) | 0.872159 | + | 0.503541i | 0.0351118 | + | 0.0202718i | 0.517453 | − | 0.855712i | \(-0.326880\pi\) |
−0.482341 | + | 0.875983i | \(0.660214\pi\) | |||||||
\(618\) | 0.530142i | 0.0213254i | ||||||||
\(619\) | 32.2683 | 1.29697 | 0.648486 | − | 0.761226i | \(-0.275402\pi\) | ||||
0.648486 | + | 0.761226i | \(0.275402\pi\) | |||||||
\(620\) | −12.0528 | − | 7.66221i | −0.484053 | − | 0.307722i | ||||
\(621\) | − | 2.02051i | − | 0.0810801i | ||||||
\(622\) | 11.4094 | − | 6.58725i | 0.457477 | − | 0.264125i | ||||
\(623\) | −45.6942 | −1.83070 | ||||||||
\(624\) | −2.76307 | + | 1.59526i | −0.110611 | + | 0.0638614i | ||||
\(625\) | −8.64085 | − | 23.4592i | −0.345634 | − | 0.938369i | ||||
\(626\) | −13.1181 | − | 22.7212i | −0.524304 | − | 0.908121i | ||||
\(627\) | 13.3542 | − | 23.1302i | 0.533316 | − | 0.923731i | ||||
\(628\) | − | 9.73484i | − | 0.388462i | ||||||
\(629\) | −26.6165 | + | 24.8158i | −1.06127 | + | 0.989470i | ||||
\(630\) | 0.349478 | − | 8.18506i | 0.0139235 | − | 0.326101i | ||||
\(631\) | −40.4578 | − | 23.3583i | −1.61060 | − | 0.929879i | −0.989231 | − | 0.146359i | \(-0.953244\pi\) |
−0.621367 | − | 0.783520i | \(-0.713422\pi\) | |||||||
\(632\) | 1.65563 | − | 0.955880i | 0.0658575 | − | 0.0380229i | ||||
\(633\) | −2.07031 | + | 1.19529i | −0.0822873 | + | 0.0475086i | ||||
\(634\) | 16.8690 | − | 9.73933i | 0.669954 | − | 0.386798i | ||||
\(635\) | 1.25836 | − | 29.4718i | 0.0499365 | − | 1.16955i | ||||
\(636\) | −3.80826 | − | 6.59610i | −0.151007 | − | 0.261552i | ||||
\(637\) | −20.4942 | −0.812009 | ||||||||
\(638\) | −15.6588 | − | 9.04059i | −0.619936 | − | 0.357920i | ||||
\(639\) | −12.6344 | −0.499811 | ||||||||
\(640\) | −2.23403 | − | 0.0953865i | −0.0883079 | − | 0.00377048i | ||||
\(641\) | 0.387440 | − | 0.671065i | 0.0153029 | − | 0.0265055i | −0.858273 | − | 0.513194i | \(-0.828462\pi\) |
0.873575 | + | 0.486689i | \(0.161795\pi\) | |||||||
\(642\) | 5.44652 | + | 9.43365i | 0.214957 | + | 0.372317i | ||||
\(643\) | 2.59452 | 0.102318 | 0.0511590 | − | 0.998691i | \(-0.483708\pi\) | ||||
0.0511590 | + | 0.998691i | \(0.483708\pi\) | |||||||
\(644\) | −6.41096 | − | 3.70137i | −0.252627 | − | 0.145854i | ||||
\(645\) | −7.01512 | − | 4.45964i | −0.276220 | − | 0.175598i | ||||
\(646\) | 29.1391 | + | 16.8234i | 1.14646 | + | 0.661910i | ||||
\(647\) | 22.2693 | + | 38.5716i | 0.875497 | + | 1.51641i | 0.856232 | + | 0.516591i | \(0.172799\pi\) |
0.0192646 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −41.5227 | − | 23.9731i | −1.62991 | − | 0.941028i | ||||
\(650\) | −9.12486 | + | 13.0852i | −0.357906 | + | 0.513243i | ||||
\(651\) | −20.2662 | − | 11.7007i | −0.794294 | − | 0.458586i | ||||
\(652\) | 8.85607 | 0.346831 | ||||||||
\(653\) | −6.19754 | − | 10.7345i | −0.242529 | − | 0.420072i | 0.718905 | − | 0.695108i | \(-0.244643\pi\) |
−0.961434 | + | 0.275036i | \(0.911310\pi\) | |||||||
\(654\) | 2.73169 | − | 4.73143i | 0.106818 | − | 0.185013i | ||||
\(655\) | 1.04645 | − | 24.5087i | 0.0408881 | − | 0.957635i | ||||
\(656\) | −0.351130 | −0.0137093 | ||||||||
\(657\) | −2.31646 | − | 1.33741i | −0.0903739 | − | 0.0521774i | ||||
\(658\) | −37.1046 | −1.44649 | ||||||||
\(659\) | −11.5002 | − | 19.9190i | −0.447985 | − | 0.775932i | 0.550270 | − | 0.834987i | \(-0.314525\pi\) |
−0.998255 | + | 0.0590544i | \(0.981191\pi\) | |||||||
\(660\) | −0.452978 | + | 10.6091i | −0.0176321 | + | 0.412959i | ||||
\(661\) | −16.4180 | + | 9.47891i | −0.638585 | + | 0.368687i | −0.784069 | − | 0.620674i | \(-0.786859\pi\) |
0.145484 | + | 0.989361i | \(0.453526\pi\) | |||||||
\(662\) | −19.2273 | + | 11.1009i | −0.747292 | + | 0.431449i | ||||
\(663\) | −16.5302 | + | 9.54370i | −0.641979 | + | 0.370647i | ||||
\(664\) | −4.66513 | − | 2.69342i | −0.181042 | − | 0.104525i | ||||
\(665\) | 46.0342 | + | 1.96552i | 1.78513 | + | 0.0762197i | ||||
\(666\) | 1.36779 | + | 5.92699i | 0.0530006 | + | 0.229666i | ||||
\(667\) | − | 7.69302i | − | 0.297875i | ||||||
\(668\) | 0.842814 | − | 1.45980i | 0.0326094 | − | 0.0564812i | ||||
\(669\) | 4.33248 | + | 7.50407i | 0.167503 | + | 0.290124i | ||||
\(670\) | 1.11234 | − | 0.580407i | 0.0429733 | − | 0.0224231i | ||||
\(671\) | −63.1803 | + | 36.4772i | −2.43905 | + | 1.40819i | ||||
\(672\) | −3.66381 | −0.141334 | ||||||||
\(673\) | −9.11651 | + | 5.26342i | −0.351416 | + | 0.202890i | −0.665309 | − | 0.746568i | \(-0.731700\pi\) |
0.313893 | + | 0.949458i | \(0.398367\pi\) | |||||||
\(674\) | − | 14.9439i | − | 0.575618i | ||||||
\(675\) | −4.10127 | − | 2.86000i | −0.157858 | − | 0.110081i | ||||
\(676\) | −2.82061 | −0.108485 | ||||||||
\(677\) | 29.3822i | 1.12925i | 0.825348 | + | 0.564625i | \(0.190979\pi\) | ||||
−0.825348 | + | 0.564625i | \(0.809021\pi\) | |||||||
\(678\) | −8.92683 | − | 5.15391i | −0.342833 | − | 0.197935i | ||||
\(679\) | 9.75826 | − | 5.63393i | 0.374488 | − | 0.216210i | ||||
\(680\) | −13.3652 | − | 0.570654i | −0.512532 | − | 0.0218836i | ||||
\(681\) | 11.0771 | + | 6.39535i | 0.424474 | + | 0.245070i | ||||
\(682\) | 26.2681 | + | 15.1659i | 1.00586 | + | 0.580733i | ||||
\(683\) | 15.2768 | − | 26.4602i | 0.584551 | − | 1.01247i | −0.410380 | − | 0.911914i | \(-0.634604\pi\) |
0.994931 | − | 0.100557i | \(-0.0320626\pi\) | |||||||
\(684\) | 4.87068 | − | 2.81209i | 0.186235 | − | 0.107523i | ||||
\(685\) | −12.1603 | + | 6.34514i | −0.464622 | + | 0.242435i | ||||
\(686\) | 1.82931 | + | 1.05615i | 0.0698433 | + | 0.0403240i | ||||
\(687\) | 12.8987 | + | 7.44705i | 0.492115 | + | 0.284123i | ||||
\(688\) | −1.85877 | + | 3.21948i | −0.0708648 | + | 0.122741i | ||||
\(689\) | 24.3006i | 0.925780i | ||||||||
\(690\) | −4.00550 | + | 2.09003i | −0.152487 | + | 0.0795661i | ||||
\(691\) | −15.2286 | + | 26.3766i | −0.579322 | + | 1.00341i | 0.416236 | + | 0.909257i | \(0.363349\pi\) |
−0.995557 | + | 0.0941578i | \(0.969984\pi\) | |||||||
\(692\) | − | 3.01434i | − | 0.114588i | ||||||
\(693\) | 17.3989i | 0.660930i | ||||||||
\(694\) | 12.2779 | − | 21.2660i | 0.466063 | − | 0.807246i | ||||
\(695\) | −36.3899 | − | 1.55374i | −1.38035 | − | 0.0589367i | ||||
\(696\) | −1.90374 | − | 3.29737i | −0.0721610 | − | 0.124986i | ||||
\(697\) | −2.10065 | −0.0795679 | ||||||||
\(698\) | −5.68801 | − | 9.85192i | −0.215294 | − | 0.372901i | ||||
\(699\) | −12.6246 | − | 21.8665i | −0.477508 | − | 0.827068i | ||||
\(700\) | −16.5877 | + | 7.77389i | −0.626958 | + | 0.293825i | ||||
\(701\) | 33.3613 | + | 19.2611i | 1.26004 | + | 0.727483i | 0.973082 | − | 0.230461i | \(-0.0740233\pi\) |
0.286956 | + | 0.957944i | \(0.407357\pi\) | |||||||
\(702\) | 3.19052i | 0.120418i | ||||||||
\(703\) | −33.3344 | + | 7.69267i | −1.25723 | + | 0.290135i | ||||
\(704\) | 4.74886 | 0.178979 | ||||||||
\(705\) | −12.1490 | + | 19.1107i | −0.457558 | + | 0.719750i | ||||
\(706\) | 3.82580 | + | 6.62648i | 0.143986 | + | 0.249391i | ||||
\(707\) | −12.3151 | + | 7.11012i | −0.463157 | + | 0.267404i | ||||
\(708\) | −5.04818 | − | 8.74371i | −0.189722 | − | 0.328609i | ||||
\(709\) | − | 38.2108i | − | 1.43504i | −0.696540 | − | 0.717518i | \(-0.745278\pi\) | ||
0.696540 | − | 0.717518i | \(-0.254722\pi\) | |||||||
\(710\) | 13.0692 | + | 25.0468i | 0.490478 | + | 0.939989i | ||||
\(711\) | − | 1.91176i | − | 0.0716966i | ||||||
\(712\) | 10.8009 | + | 6.23589i | 0.404780 | + | 0.233700i | ||||
\(713\) | 12.9053i | 0.483308i | ||||||||
\(714\) | −21.9189 | −0.820293 | ||||||||
\(715\) | 18.1759 | − | 28.5911i | 0.679739 | − | 1.06925i | ||||
\(716\) | 13.7907 | − | 7.96205i | 0.515382 | − | 0.297556i | ||||
\(717\) | −29.7563 | −1.11127 | ||||||||
\(718\) | −7.80583 | + | 13.5201i | −0.291311 | + | 0.504565i | ||||
\(719\) | 13.7643 | − | 23.8404i | 0.513321 | − | 0.889099i | −0.486559 | − | 0.873648i | \(-0.661748\pi\) |
0.999881 | − | 0.0154510i | \(-0.00491840\pi\) | |||||||
\(720\) | −1.19962 | + | 1.88704i | −0.0447073 | + | 0.0703257i | ||||
\(721\) | 1.68211 | − | 0.971168i | 0.0626451 | − | 0.0361682i | ||||
\(722\) | 6.31568 | + | 10.9391i | 0.235045 | + | 0.407110i | ||||
\(723\) | 10.8976 | − | 18.8752i | 0.405287 | − | 0.701978i | ||||
\(724\) | 7.78303 | − | 13.4806i | 0.289254 | − | 0.501003i | ||||
\(725\) | −15.6155 | − | 10.8894i | −0.579945 | − | 0.404421i | ||||
\(726\) | − | 11.5517i | − | 0.428724i | ||||||
\(727\) | −21.7742 | − | 37.7140i | −0.807560 | − | 1.39874i | −0.914549 | − | 0.404476i | \(-0.867454\pi\) |
0.106988 | − | 0.994260i | \(-0.465879\pi\) | |||||||
\(728\) | 10.1233 | + | 5.84471i | 0.375196 | + | 0.216619i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.255142 | + | 5.97564i | −0.00944323 | + | 0.221168i | ||||
\(731\) | −11.1202 | + | 19.2607i | −0.411294 | + | 0.712382i | ||||
\(732\) | −15.3625 | −0.567814 | ||||||||
\(733\) | 12.3778 | − | 7.14631i | 0.457183 | − | 0.263955i | −0.253676 | − | 0.967289i | \(-0.581640\pi\) |
0.710859 | + | 0.703334i | \(0.248306\pi\) | |||||||
\(734\) | − | 17.6046i | − | 0.649798i | ||||||
\(735\) | −12.7340 | + | 6.64449i | −0.469702 | + | 0.245086i | ||||
\(736\) | 1.01025 | + | 1.74981i | 0.0372384 | + | 0.0644988i | ||||
\(737\) | −2.30760 | + | 1.33229i | −0.0850016 | + | 0.0490757i | ||||
\(738\) | −0.175565 | + | 0.304088i | −0.00646264 | + | 0.0111936i | ||||
\(739\) | −42.6664 | −1.56951 | −0.784755 | − | 0.619807i | \(-0.787211\pi\) | ||||
−0.784755 | + | 0.619807i | \(0.787211\pi\) | |||||||
\(740\) | 10.3349 | − | 8.84246i | 0.379920 | − | 0.325055i | ||||
\(741\) | −17.9440 | −0.659190 | ||||||||
\(742\) | −13.9527 | + | 24.1668i | −0.512221 | + | 0.887192i | ||||
\(743\) | 21.8263 | − | 12.6014i | 0.800728 | − | 0.462301i | −0.0429974 | − | 0.999075i | \(-0.513691\pi\) |
0.843726 | + | 0.536774i | \(0.180357\pi\) | |||||||
\(744\) | 3.19359 | + | 5.53146i | 0.117083 | + | 0.202793i | ||||
\(745\) | 10.8257 | + | 20.7472i | 0.396623 | + | 0.760120i | ||||
\(746\) | 32.1477i | 1.17701i | ||||||||
\(747\) | −4.66513 | + | 2.69342i | −0.170688 | + | 0.0985469i | ||||
\(748\) | 28.4103 | 1.03878 | ||||||||
\(749\) | 19.9550 | − | 34.5631i | 0.729140 | − | 1.26291i | ||||
\(750\) | −1.42733 | + | 11.0889i | −0.0521186 | + | 0.404908i | ||||
\(751\) | −5.81907 | −0.212341 | −0.106170 | − | 0.994348i | \(-0.533859\pi\) | ||||
−0.106170 | + | 0.994348i | \(0.533859\pi\) | |||||||
\(752\) | 8.77054 | + | 5.06368i | 0.319829 | + | 0.184653i | ||||
\(753\) | 9.74370 | + | 16.8766i | 0.355080 | + | 0.615017i | ||||
\(754\) | 12.1478i | 0.442397i | ||||||||
\(755\) | −3.28080 | + | 5.16077i | −0.119400 | + | 0.187820i | ||||
\(756\) | −1.83190 | + | 3.17295i | −0.0666257 | + | 0.115399i | ||||
\(757\) | 18.4252 | − | 31.9134i | 0.669675 | − | 1.15991i | −0.308320 | − | 0.951283i | \(-0.599767\pi\) |
0.977995 | − | 0.208628i | \(-0.0668998\pi\) | |||||||
\(758\) | 1.28515 | + | 2.22595i | 0.0466788 | + | 0.0808501i | ||||
\(759\) | 8.30961 | − | 4.79755i | 0.301620 | − | 0.174140i | ||||
\(760\) | −10.6130 | − | 6.74689i | −0.384975 | − | 0.244736i | ||||
\(761\) | −0.855195 | + | 1.48124i | −0.0310008 | + | 0.0536950i | −0.881110 | − | 0.472912i | \(-0.843203\pi\) |
0.850109 | + | 0.526607i | \(0.176536\pi\) | |||||||
\(762\) | −6.59611 | + | 11.4248i | −0.238952 | + | 0.413877i | ||||
\(763\) | −20.0168 | −0.724655 | ||||||||
\(764\) | 21.4352 | − | 12.3756i | 0.775499 | − | 0.447734i | ||||
\(765\) | −7.17680 | + | 11.2893i | −0.259478 | + | 0.408165i | ||||
\(766\) | −19.6329 | −0.709364 | ||||||||
\(767\) | 32.2126i | 1.16313i | ||||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 8.99578i | 0.324396i | 0.986758 | + | 0.162198i | \(0.0518584\pi\) | ||||
−0.986758 | + | 0.162198i | \(0.948142\pi\) | |||||||
\(770\) | 34.4920 | − | 17.9976i | 1.24300 | − | 0.648588i | ||||
\(771\) | − | 31.1443i | − | 1.12163i | ||||||
\(772\) | −0.676615 | − | 1.17193i | −0.0243519 | − | 0.0421788i | ||||
\(773\) | −27.7028 | + | 15.9942i | −0.996400 | + | 0.575272i | −0.907181 | − | 0.420740i | \(-0.861770\pi\) |
−0.0892191 | + | 0.996012i | \(0.528437\pi\) | |||||||
\(774\) | 1.85877 | + | 3.21948i | 0.0668120 | + | 0.115722i | ||||
\(775\) | 26.1955 | + | 18.2673i | 0.940972 | + | 0.656181i | ||||
\(776\) | −3.07545 | −0.110402 | ||||||||
\(777\) | 16.3004 | − | 15.1976i | 0.584772 | − | 0.545210i | ||||
\(778\) | − | 21.6972i | − | 0.777882i | ||||||
\(779\) | −1.71024 | − | 0.987409i | −0.0612758 | − | 0.0353776i | ||||
\(780\) | 6.32495 | − | 3.30030i | 0.226469 | − | 0.118170i | ||||
\(781\) | −29.9996 | − | 51.9609i | −1.07347 | − | 1.85931i | ||||
\(782\) | 6.04388 | + | 10.4683i | 0.216129 | + | 0.374346i | ||||
\(783\) | −3.80747 | −0.136068 | ||||||||
\(784\) | 3.21173 | + | 5.56289i | 0.114705 | + | 0.198675i | ||||
\(785\) | −0.928572 | + | 21.7479i | −0.0331422 | + | 0.776218i | ||||
\(786\) | −5.48531 | + | 9.50083i | −0.195654 | + | 0.338883i | ||||
\(787\) | − | 12.5293i | − | 0.446623i | −0.974747 | − | 0.223311i | \(-0.928313\pi\) | ||
0.974747 | − | 0.223311i | \(-0.0716866\pi\) | |||||||
\(788\) | − | 13.2852i | − | 0.473266i | ||||||
\(789\) | 1.15216 | − | 1.99559i | 0.0410178 | − | 0.0710449i | ||||
\(790\) | −3.78991 | + | 1.97754i | −0.134839 | + | 0.0703578i | ||||
\(791\) | 37.7658i | 1.34280i | ||||||||
\(792\) | 2.37443 | − | 4.11264i | 0.0843717 | − | 0.146136i | ||||
\(793\) | 42.4476 | + | 24.5071i | 1.50736 | + | 0.870274i | ||||
\(794\) | 12.8826 | + | 7.43775i | 0.457185 | + | 0.263956i | ||||
\(795\) | 7.87860 | + | 15.0992i | 0.279425 | + | 0.535512i | ||||
\(796\) | 2.33221 | − | 1.34650i | 0.0826629 | − | 0.0477254i | ||||
\(797\) | 21.0287 | − | 36.4227i | 0.744873 | − | 1.29016i | −0.205381 | − | 0.978682i | \(-0.565843\pi\) |
0.950254 | − | 0.311476i | \(-0.100823\pi\) | |||||||
\(798\) | −17.8452 | − | 10.3029i | −0.631714 | − | 0.364720i | ||||
\(799\) | 52.4702 | + | 30.2937i | 1.85626 | + | 1.07171i | ||||
\(800\) | 4.98180 | + | 0.426193i | 0.176133 | + | 0.0150682i | ||||
\(801\) | 10.8009 | − | 6.23589i | 0.381630 | − | 0.220334i | ||||
\(802\) | 8.23021 | + | 4.75171i | 0.290619 | + | 0.167789i | ||||
\(803\) | − | 12.7024i | − | 0.448257i | ||||||
\(804\) | −0.561100 | −0.0197885 | ||||||||
\(805\) | 13.9692 | + | 8.88050i | 0.492351 | + | 0.312997i | ||||
\(806\) | − | 20.3784i | − | 0.717798i | ||||||
\(807\) | −15.6098 | + | 9.01232i | −0.549491 | + | 0.317249i | ||||
\(808\) | 3.88128 | 0.136543 | ||||||||
\(809\) | 15.4715 | − | 8.93247i | 0.543949 | − | 0.314049i | −0.202729 | − | 0.979235i | \(-0.564981\pi\) |
0.746678 | + | 0.665186i | \(0.231648\pi\) | |||||||
\(810\) | 1.03441 | + | 1.98242i | 0.0363454 | + | 0.0696552i | ||||
\(811\) | 19.3863 | + | 33.5781i | 0.680746 | + | 1.17909i | 0.974753 | + | 0.223284i | \(0.0716778\pi\) |
−0.294007 | + | 0.955803i | \(0.594989\pi\) | |||||||
\(812\) | −6.97492 | + | 12.0809i | −0.244772 | + | 0.423957i | ||||
\(813\) | − | 29.4791i | − | 1.03388i | ||||||
\(814\) | −21.1278 | + | 19.6984i | −0.740530 | + | 0.690430i | ||||
\(815\) | −19.7848 | − | 0.844750i | −0.693030 | − | 0.0295903i | ||||
\(816\) | 5.18104 | + | 2.99127i | 0.181373 | + | 0.104715i | ||||
\(817\) | −18.1069 | + | 10.4540i | −0.633480 | + | 0.365740i | ||||
\(818\) | −8.91611 | + | 5.14772i | −0.311744 | + | 0.179986i | ||||
\(819\) | 10.1233 | − | 5.84471i | 0.353738 | − | 0.204231i | ||||
\(820\) | 0.784436 | + | 0.0334931i | 0.0273937 | + | 0.00116963i | ||||
\(821\) | 1.62312 | + | 2.81133i | 0.0566474 | + | 0.0981162i | 0.892958 | − | 0.450139i | \(-0.148626\pi\) |
−0.836311 | + | 0.548255i | \(0.815292\pi\) | |||||||
\(822\) | 6.13407 | 0.213950 | ||||||||
\(823\) | −19.0170 | − | 10.9795i | −0.662891 | − | 0.382720i | 0.130487 | − | 0.991450i | \(-0.458346\pi\) |
−0.793378 | + | 0.608730i | \(0.791679\pi\) | |||||||
\(824\) | −0.530142 | −0.0184684 | ||||||||
\(825\) | 2.02393 | − | 23.6579i | 0.0704643 | − | 0.823662i | ||||
\(826\) | −18.4956 | + | 32.0352i | −0.643543 | + | 1.11465i | ||||
\(827\) | −1.46864 | − | 2.54376i | −0.0510697 | − | 0.0884553i | 0.839360 | − | 0.543575i | \(-0.182930\pi\) |
−0.890430 | + | 0.455120i | \(0.849596\pi\) | |||||||
\(828\) | 2.02051 | 0.0702174 | ||||||||
\(829\) | 18.7064 | + | 10.8001i | 0.649698 | + | 0.375104i | 0.788341 | − | 0.615239i | \(-0.210940\pi\) |
−0.138642 | + | 0.990343i | \(0.544274\pi\) | |||||||
\(830\) | 10.1651 | + | 6.46217i | 0.352837 | + | 0.224305i | ||||
\(831\) | −3.41686 | − | 1.97273i | −0.118530 | − | 0.0684331i | ||||
\(832\) | −1.59526 | − | 2.76307i | −0.0553056 | − | 0.0957921i | ||||
\(833\) | 19.2143 | + | 33.2802i | 0.665738 | + | 1.15309i | ||||
\(834\) | 14.1066 | + | 8.14444i | 0.488471 | + | 0.282019i | ||||
\(835\) | −2.02212 | + | 3.18084i | −0.0699783 | + | 0.110077i | ||||
\(836\) | 23.1302 | + | 13.3542i | 0.799974 | + | 0.461865i | ||||
\(837\) | 6.38718 | 0.220773 | ||||||||
\(838\) | −1.35626 | − | 2.34912i | −0.0468514 | − | 0.0811489i | ||||
\(839\) | 5.42564 | − | 9.39749i | 0.187314 | − | 0.324437i | −0.757040 | − | 0.653369i | \(-0.773355\pi\) |
0.944354 | + | 0.328931i | \(0.106688\pi\) | |||||||
\(840\) | 8.18506 | + | 0.349478i | 0.282411 | + | 0.0120581i | ||||
\(841\) | 14.5031 | 0.500108 | ||||||||
\(842\) | −34.1092 | − | 19.6929i | −1.17548 | − | 0.678664i | ||||
\(843\) | 32.0268 | 1.10306 | ||||||||
\(844\) | −1.19529 | − | 2.07031i | −0.0411436 | − | 0.0712629i | ||||
\(845\) | 6.30134 | + | 0.269048i | 0.216773 | + | 0.00925555i | ||||
\(846\) | 8.77054 | − | 5.06368i | 0.301537 | − | 0.174093i | ||||
\(847\) | −36.6529 | + | 21.1616i | −1.25941 | + | 0.727121i | ||||
\(848\) | 6.59610 | − | 3.80826i | 0.226511 | − | 0.130776i | ||||
\(849\) | −5.15654 | − | 2.97713i | −0.176972 | − | 0.102175i | ||||
\(850\) | 29.8039 | + | 2.54972i | 1.02226 | + | 0.0874547i | ||||
\(851\) | −11.7529 | − | 3.59439i | −0.402884 | − | 0.123214i | ||||
\(852\) | − | 12.6344i | − | 0.432849i | ||||||
\(853\) | −18.5925 | + | 32.2032i | −0.636596 | + | 1.10262i | 0.349578 | + | 0.936907i | \(0.386325\pi\) |
−0.986175 | + | 0.165710i | \(0.947008\pi\) | |||||||
\(854\) | 28.1426 | + | 48.7444i | 0.963020 | + | 1.66800i | ||||
\(855\) | −11.1495 | + | 5.81770i | −0.381305 | + | 0.198961i | ||||
\(856\) | −9.43365 | + | 5.44652i | −0.322436 | + | 0.186158i | ||||
\(857\) | 38.8711 | 1.32781 | 0.663906 | − | 0.747816i | \(-0.268898\pi\) | ||||
0.663906 | + | 0.747816i | \(0.268898\pi\) | |||||||
\(858\) | −13.1214 | + | 7.57566i | −0.447958 | + | 0.258629i | ||||
\(859\) | 28.0021i | 0.955419i | 0.878518 | + | 0.477710i | \(0.158533\pi\) | ||||
−0.878518 | + | 0.477710i | \(0.841467\pi\) | |||||||
\(860\) | 4.45964 | − | 7.01512i | 0.152072 | − | 0.239213i | ||||
\(861\) | 1.28647 | 0.0438429 | ||||||||
\(862\) | 22.8474i | 0.778186i | ||||||||
\(863\) | 45.3792 | + | 26.1997i | 1.54473 | + | 0.891848i | 0.998531 | + | 0.0541894i | \(0.0172575\pi\) |
0.546195 | + | 0.837658i | \(0.316076\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | −0.287528 | + | 6.73414i | −0.00977624 | + | 0.228968i | ||||
\(866\) | 10.0726 | + | 5.81541i | 0.342280 | + | 0.197616i | ||||
\(867\) | 16.2733 | + | 9.39542i | 0.552672 | + | 0.319085i | ||||
\(868\) | 11.7007 | − | 20.2662i | 0.397147 | − | 0.687879i | ||||
\(869\) | 7.86237 | − | 4.53934i | 0.266713 | − | 0.153987i | ||||
\(870\) | 3.93849 | + | 7.54802i | 0.133527 | + | 0.255902i | ||||
\(871\) | 1.55036 | + | 0.895099i | 0.0525319 | + | 0.0303293i | ||||
\(872\) | 4.73143 | + | 2.73169i | 0.160226 | + | 0.0925067i | ||||
\(873\) | −1.53773 | + | 2.66342i | −0.0520442 | + | 0.0901432i | ||||
\(874\) | 11.3637i | 0.384382i | ||||||||
\(875\) | 37.7991 | − | 15.7849i | 1.27784 | − | 0.533626i | ||||
\(876\) | 1.33741 | − | 2.31646i | 0.0451869 | − | 0.0782661i | ||||
\(877\) | − | 14.7977i | − | 0.499684i | −0.968287 | − | 0.249842i | \(-0.919621\pi\) | ||
0.968287 | − | 0.249842i | \(-0.0803787\pi\) | |||||||
\(878\) | 18.7920i | 0.634199i | ||||||||
\(879\) | −8.24771 | + | 14.2855i | −0.278188 | + | 0.481836i | ||||
\(880\) | −10.6091 | − | 0.452978i | −0.357633 | − | 0.0152699i | ||||
\(881\) | −16.0825 | − | 27.8557i | −0.541833 | − | 0.938482i | −0.998799 | − | 0.0489975i | \(-0.984397\pi\) |
0.456966 | − | 0.889484i | \(-0.348936\pi\) | |||||||
\(882\) | 6.42347 | 0.216289 | ||||||||
\(883\) | −7.17561 | − | 12.4285i | −0.241478 | − | 0.418253i | 0.719657 | − | 0.694329i | \(-0.244299\pi\) |
−0.961136 | + | 0.276077i | \(0.910966\pi\) | |||||||
\(884\) | −9.54370 | − | 16.5302i | −0.320989 | − | 0.555970i | ||||
\(885\) | 10.4438 | + | 20.0153i | 0.351064 | + | 0.672806i | ||||
\(886\) | −5.31781 | − | 3.07024i | −0.178655 | − | 0.103147i | ||||
\(887\) | − | 27.5684i | − | 0.925658i | −0.886448 | − | 0.462829i | \(-0.846834\pi\) | ||
0.886448 | − | 0.462829i | \(-0.153166\pi\) | |||||||
\(888\) | −5.92699 | + | 1.36779i | −0.198897 | + | 0.0458999i | ||||
\(889\) | 48.3337 | 1.62106 | ||||||||
\(890\) | −23.5347 | − | 14.9614i | −0.788885 | − | 0.501509i | ||||
\(891\) | −2.37443 | − | 4.11264i | −0.0795464 | − | 0.137778i | ||||
\(892\) | −7.50407 | + | 4.33248i | −0.251255 | + | 0.145062i | ||||
\(893\) | 28.4790 | + | 49.3271i | 0.953013 | + | 1.65067i | ||||
\(894\) | − | 10.4656i | − | 0.350022i | ||||||
\(895\) | −31.5683 | + | 16.4720i | −1.05521 | + | 0.550599i | ||||
\(896\) | − | 3.66381i | − | 0.122399i | ||||||
\(897\) | −5.58279 | − | 3.22323i | −0.186404 | − | 0.107620i | ||||
\(898\) | − | 10.6968i | − | 0.356956i | ||||||
\(899\) | 24.3190 | 0.811084 | ||||||||
\(900\) | 2.86000 | − | 4.10127i | 0.0953332 | − | 0.136709i | ||||
\(901\) | 39.4615 | − | 22.7831i | 1.31465 | − | 0.759015i | ||||
\(902\) | −1.66747 | −0.0555207 | ||||||||
\(903\) | 6.81016 | − | 11.7955i | 0.226628 | − | 0.392531i | ||||
\(904\) | 5.15391 | − | 8.92683i | 0.171417 | − | 0.296902i | ||||
\(905\) | −18.6734 | + | 29.3737i | −0.620725 | + | 0.976415i | ||||
\(906\) | 2.36845 | − | 1.36743i | 0.0786866 | − | 0.0454297i | ||||
\(907\) | −11.1954 | − | 19.3910i | −0.371737 | − | 0.643868i | 0.618096 | − | 0.786103i | \(-0.287904\pi\) |
−0.989833 | + | 0.142235i | \(0.954571\pi\) | |||||||
\(908\) | −6.39535 | + | 11.0771i | −0.212237 | + | 0.367606i | ||||
\(909\) | 1.94064 | − | 3.36129i | 0.0643669 | − | 0.111487i | ||||
\(910\) | −22.0584 | − | 14.0229i | −0.731228 | − | 0.464855i | ||||
\(911\) | 22.2940i | 0.738633i | 0.929304 | + | 0.369317i | \(0.120408\pi\) | ||||
−0.929304 | + | 0.369317i | \(0.879592\pi\) | |||||||
\(912\) | 2.81209 | + | 4.87068i | 0.0931175 | + | 0.161284i | ||||
\(913\) | −22.1541 | − | 12.7907i | −0.733193 | − | 0.423309i | ||||
\(914\) | −37.7843 | −1.24979 | ||||||||
\(915\) | 34.3203 | + | 1.46537i | 1.13459 | + | 0.0484438i | ||||
\(916\) | −7.44705 | + | 12.8987i | −0.246057 | + | 0.426184i | ||||
\(917\) | 40.1942 | 1.32733 | ||||||||
\(918\) | 5.18104 | − | 2.99127i | 0.171000 | − | 0.0987267i | ||||
\(919\) | 41.0031i | 1.35257i | 0.736642 | + | 0.676283i | \(0.236410\pi\) | ||||
−0.736642 | + | 0.676283i | \(0.763590\pi\) | |||||||
\(920\) | −2.09003 | − | 4.00550i | −0.0689062 | − | 0.132057i | ||||
\(921\) | −4.95267 | − | 8.57827i | −0.163196 | − | 0.282664i | ||||
\(922\) | 30.1115 | − | 17.3849i | 0.991668 | − | 0.572540i | ||||
\(923\) | −20.1552 | + | 34.9098i | −0.663416 | + | 1.14907i | ||||
\(924\) | −17.3989 | −0.572382 | ||||||||
\(925\) | −23.9320 | + | 18.7685i | −0.786881 | + | 0.617105i | ||||
\(926\) | −27.5870 | −0.906566 | ||||||||
\(927\) | −0.265071 | + | 0.459116i | −0.00870607 | + | 0.0150794i | ||||
\(928\) | 3.29737 | − | 1.90374i | 0.108241 | − | 0.0624932i | ||||
\(929\) | 22.0138 | + | 38.1290i | 0.722248 | + | 1.25097i | 0.960097 | + | 0.279668i | \(0.0902244\pi\) |
−0.237849 | + | 0.971302i | \(0.576442\pi\) | |||||||
\(930\) | −6.60695 | − | 12.6621i | −0.216651 | − | 0.415206i | ||||
\(931\) | 36.1267i | 1.18401i | ||||||||
\(932\) | 21.8665 | − | 12.6246i | 0.716261 | − | 0.413534i | ||||
\(933\) | 13.1745 | 0.431314 | ||||||||
\(934\) | −3.03050 | + | 5.24898i | −0.0991609 | + | 0.171752i | ||||
\(935\) | −63.4695 | − | 2.70996i | −2.07567 | − | 0.0886251i | ||||
\(936\) | −3.19052 | −0.104285 | ||||||||
\(937\) | −23.7712 | − | 13.7243i | −0.776570 | − | 0.448353i | 0.0586433 | − | 0.998279i | \(-0.481323\pi\) |
−0.835213 | + | 0.549926i | \(0.814656\pi\) | |||||||
\(938\) | 1.02788 | + | 1.78034i | 0.0335615 | + | 0.0581302i | ||||
\(939\) | − | 26.2362i | − | 0.856185i | ||||||
\(940\) | −19.1107 | − | 12.1490i | −0.623321 | − | 0.396257i | ||||
\(941\) | 24.9629 | − | 43.2370i | 0.813767 | − | 1.40949i | −0.0964430 | − | 0.995339i | \(-0.530747\pi\) |
0.910210 | − | 0.414147i | \(-0.135920\pi\) | |||||||
\(942\) | 4.86742 | − | 8.43062i | 0.158589 | − | 0.274684i | ||||
\(943\) | −0.354730 | − | 0.614411i | −0.0115516 | − | 0.0200080i | ||||
\(944\) | 8.74371 | − | 5.04818i | 0.284584 | − | 0.164304i | ||||
\(945\) | 4.39519 | − | 6.91373i | 0.142975 | − | 0.224904i | ||||
\(946\) | −8.82702 | + | 15.2889i | −0.286991 | + | 0.497084i | ||||
\(947\) | 0.600066 | − | 1.03934i | 0.0194995 | − | 0.0337742i | −0.856111 | − | 0.516792i | \(-0.827126\pi\) |
0.875611 | + | 0.483018i | \(0.160459\pi\) | |||||||
\(948\) | 1.91176 | 0.0620911 | ||||||||
\(949\) | −7.39071 | + | 4.26703i | −0.239913 | + | 0.138514i | ||||
\(950\) | 23.0663 | + | 16.0851i | 0.748369 | + | 0.521870i | ||||
\(951\) | 19.4787 | 0.631639 | ||||||||
\(952\) | − | 21.9189i | − | 0.710395i | ||||||
\(953\) | −39.8269 | − | 22.9941i | −1.29012 | − | 0.744851i | −0.311445 | − | 0.950264i | \(-0.600813\pi\) |
−0.978675 | + | 0.205413i | \(0.934146\pi\) | |||||||
\(954\) | − | 7.61652i | − | 0.246594i | ||||||
\(955\) | −49.0674 | + | 25.6029i | −1.58778 | + | 0.828491i | ||||
\(956\) | − | 29.7563i | − | 0.962386i | ||||||
\(957\) | −9.04059 | − | 15.6588i | −0.292241 | − | 0.506176i | ||||
\(958\) | 23.5812 | − | 13.6146i | 0.761874 | − | 0.439868i | ||||
\(959\) | −11.2370 | − | 19.4631i | −0.362862 | − | 0.628496i | ||||
\(960\) | −1.88704 | − | 1.19962i | −0.0609038 | − | 0.0387177i | ||||
\(961\) | −9.79601 | −0.316000 | ||||||||
\(962\) | 18.5586 | + | 5.67578i | 0.598354 | + | 0.182995i | ||||
\(963\) | 10.8930i | 0.351023i | ||||||||
\(964\) | 18.8752 | + | 10.8976i | 0.607931 | + | 0.350989i | ||||
\(965\) | 1.39979 | + | 2.68267i | 0.0450610 | + | 0.0863583i | ||||
\(966\) | −3.70137 | − | 6.41096i | −0.119090 | − | 0.206269i | ||||
\(967\) | 29.9323 | + | 51.8443i | 0.962558 | + | 1.66720i | 0.716038 | + | 0.698061i | \(0.245954\pi\) |
0.246520 | + | 0.969138i | \(0.420713\pi\) | |||||||
\(968\) | 11.5517 | 0.371286 | ||||||||
\(969\) | 16.8234 | + | 29.1391i | 0.540447 | + | 0.936081i | ||||
\(970\) | 6.87066 | + | 0.293357i | 0.220604 | + | 0.00941912i | ||||
\(971\) | 20.0472 | − | 34.7228i | 0.643346 | − | 1.11431i | −0.341335 | − | 0.939942i | \(-0.610879\pi\) |
0.984681 | − | 0.174366i | \(-0.0557877\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 59.6793i | − | 1.91323i | ||||||
\(974\) | 8.24629 | − | 14.2830i | 0.264228 | − | 0.457656i | ||||
\(975\) | −14.4449 | + | 6.76966i | −0.462608 | + | 0.216803i | ||||
\(976\) | − | 15.3625i | − | 0.491741i | ||||||
\(977\) | 23.2371 | − | 40.2479i | 0.743422 | − | 1.28764i | −0.207506 | − | 0.978234i | \(-0.566535\pi\) |
0.950928 | − | 0.309411i | \(-0.100132\pi\) | |||||||
\(978\) | 7.66959 | + | 4.42804i | 0.245246 | + | 0.141593i | ||||
\(979\) | 51.2919 | + | 29.6134i | 1.63930 | + | 0.946448i | ||||
\(980\) | −6.64449 | − | 12.7340i | −0.212251 | − | 0.406774i | ||||
\(981\) | 4.73143 | − | 2.73169i | 0.151063 | − | 0.0872161i | ||||
\(982\) | −9.25250 | + | 16.0258i | −0.295259 | + | 0.511404i | ||||
\(983\) | −38.9148 | − | 22.4675i | −1.24119 | − | 0.716602i | −0.271854 | − | 0.962339i | \(-0.587637\pi\) |
−0.969337 | + | 0.245737i | \(0.920970\pi\) | |||||||
\(984\) | −0.304088 | − | 0.175565i | −0.00969396 | − | 0.00559681i | ||||
\(985\) | −1.26723 | + | 29.6796i | −0.0403773 | + | 0.945671i | ||||
\(986\) | 19.7267 | − | 11.3892i | 0.628225 | − | 0.362706i | ||||
\(987\) | −32.1336 | − | 18.5523i | −1.02282 | − | 0.590527i | ||||
\(988\) | − | 17.9440i | − | 0.570875i | ||||||
\(989\) | −7.51130 | −0.238845 | ||||||||
\(990\) | −5.69685 | + | 8.96127i | −0.181058 | + | 0.284808i | ||||
\(991\) | 54.6485i | 1.73597i | 0.496594 | + | 0.867983i | \(0.334584\pi\) | ||||
−0.496594 | + | 0.867983i | \(0.665416\pi\) | |||||||
\(992\) | −5.53146 | + | 3.19359i | −0.175624 | + | 0.101397i | ||||
\(993\) | −22.2018 | −0.704553 | ||||||||
\(994\) | −40.0884 | + | 23.1451i | −1.27153 | + | 0.734117i | ||||
\(995\) | −5.33866 | + | 2.78566i | −0.169247 | + | 0.0883115i | ||||
\(996\) | −2.69342 | − | 4.66513i | −0.0853441 | − | 0.147820i | ||||
\(997\) | 21.5625 | − | 37.3473i | 0.682891 | − | 1.18280i | −0.291204 | − | 0.956661i | \(-0.594056\pi\) |
0.974095 | − | 0.226141i | \(-0.0726109\pi\) | |||||||
\(998\) | 26.3802i | 0.835052i | ||||||||
\(999\) | −1.77896 | + | 5.81681i | −0.0562836 | + | 0.184036i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.ba.a.619.8 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.b.619.11 | yes | 36 | ||
37.11 | even | 6 | 1110.2.ba.b.529.11 | yes | 36 | ||
185.159 | even | 6 | inner | 1110.2.ba.a.529.8 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.8 | ✓ | 36 | 185.159 | even | 6 | inner | |
1110.2.ba.a.619.8 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.529.11 | yes | 36 | 37.11 | even | 6 | ||
1110.2.ba.b.619.11 | yes | 36 | 5.4 | even | 2 |